{"id":3434,"date":"2024-09-04T13:05:34","date_gmt":"2024-09-04T13:05:34","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=3434"},"modified":"2025-08-13T15:35:31","modified_gmt":"2025-08-13T15:35:31","slug":"linear-equations-and-inequalities-get-stronger-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/linear-equations-and-inequalities-get-stronger-2\/","title":{"raw":"Linear Equations and Inequalities: Get Stronger","rendered":"Linear Equations and Inequalities: Get Stronger"},"content":{"raw":"<h2><span data-sheets-root=\"1\">Graphing and Analyzing Linear Equations<\/span><\/h2>\r\nFor each of the following exercises, find the [latex]x[\/latex]-intercept and the [latex]y[\/latex]-intercept without graphing. Write the coordinates of each intercept.\r\n<ol>\r\n \t<li>[latex] y = -3x + 6 [\/latex]<\/li>\r\n \t<li>[latex] 3x - 2y = 6 [\/latex]<\/li>\r\n \t<li>[latex] 3x + 8y = 9 [\/latex]<\/li>\r\n<\/ol>\r\nFor each of the following exercises, solve the equation for [latex]y[\/latex] in terms of [latex]x[\/latex].\r\n<ol start=\"4\">\r\n \t<li>[latex] 4x + 2y = 8 [\/latex]<\/li>\r\n \t<li>[latex] 2x = 5 - 3y [\/latex]<\/li>\r\n \t<li>[latex] 5y + 4 = 10x [\/latex]<\/li>\r\n<\/ol>\r\nFor each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers.\r\n<ol start=\"7\">\r\n \t<li>[latex] (-4, 1) \\text{ and } (3, -4) [\/latex]<\/li>\r\n \t<li>[latex] (5, 0) \\text{ and } (5, 6) [\/latex]<\/li>\r\n \t<li>Find the distance between the two given points [latex] (19, 12) \\text{ and } (41, 71) [\/latex] using your calculator, and round your answer to the nearest hundredth.<\/li>\r\n<\/ol>\r\nFor each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points.\r\n<ol start=\"10\">\r\n \t<li>[latex] (-1, 1) \\text{ and } (7, -4) [\/latex]<\/li>\r\n \t<li>[latex] (0, 7) \\text{ and } (4, -9) [\/latex]<\/li>\r\n<\/ol>\r\nFor each of the following exercises, identify the information requested.\r\n<ol start=\"12\">\r\n \t<li>What are the coordinates of the origin?<\/li>\r\n \t<li>If a point is located on the y-axis, what is the x-coordinate?<\/li>\r\n \t<li>If a point is located on the x-axis, what is the y-coordinate?<\/li>\r\n<\/ol>\r\nFor each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line).\r\n<ol start=\"15\">\r\n \t<li>[latex] (-1, 2), (0, 4), (2, 1) [\/latex]\r\n\r\n[caption id=\"attachment_5226\" align=\"alignnone\" width=\"288\"]<img class=\"wp-image-5226 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89-288x300.jpeg\" alt=\"\" width=\"288\" height=\"300\" \/> Empty coordinate plane[\/caption]<\/li>\r\n \t<li>Name the coordinates of the points graphed.\r\n\r\n[caption id=\"attachment_5227\" align=\"alignnone\" width=\"288\"]<img class=\"wp-image-5227 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8-288x300.jpeg\" alt=\"\" width=\"288\" height=\"300\" \/> Coordinate plane with points A,B,C[\/caption]<\/li>\r\n<\/ol>\r\nFor each of the following exercises, construct a table and graph the equation by plotting at least three points.\r\n<ol start=\"17\">\r\n \t<li>[latex] y = \\frac{1}{3}x + 2 [\/latex]<\/li>\r\n \t<li>[latex] 2y = x + 3 [\/latex]<\/li>\r\n<\/ol>\r\nFor each of the following exercises, find and plot the [latex]x[\/latex]- and [latex]y[\/latex]-intercepts, and graph the straight line based on those two points.\r\n<ol start=\"19\">\r\n \t<li>[latex] x - 2y = 8 [\/latex]<\/li>\r\n \t<li>[latex] 3y = -2x + 6 [\/latex]<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_5228\" align=\"alignnone\" width=\"288\"]<img class=\"wp-image-5228 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad-288x300.jpeg\" alt=\"\" width=\"288\" height=\"300\" \/> Coordinate plane with line segment[\/caption]\r\n\r\nFor each of the following exercises, use the graph in the figure below.\r\n<ol start=\"21\">\r\n \t<li>Find the distance between the two endpoints using the distance formula. Round to three decimal places.<\/li>\r\n \t<li>Find the coordinates of the midpoint of the line segment connecting the two points.<\/li>\r\n \t<li>Find the distance that [latex] (-3, 4) [\/latex] is from the origin.<\/li>\r\n \t<li>Find the distance that [latex] (5, 2) [\/latex] is from the origin. Round to three decimal places.<\/li>\r\n \t<li>Which point is closer to the origin?<\/li>\r\n<\/ol>\r\nFor the following exercises, find the slope of the line that passes through the given points.\r\n<ol start=\"26\">\r\n \t<li>[latex] (5, 4) [\/latex] and [latex] (7, 9) [\/latex]<\/li>\r\n \t<li>[latex] (-3, 2) [\/latex] and [latex] (4, -7) [\/latex]<\/li>\r\n \t<li>[latex] (-5, 4) [\/latex] and [latex] (2, 4) [\/latex]<\/li>\r\n \t<li>[latex] (-1, -2) [\/latex] and [latex] (3, 4) [\/latex]<\/li>\r\n \t<li>[latex] (3, -2) [\/latex] and [latex] (3, -2) [\/latex]<\/li>\r\n<\/ol>\r\n<h2><span data-sheets-root=\"1\">Equations of Lines<\/span><\/h2>\r\nFor the following exercises, solve the equation for [latex]x[\/latex].\r\n<ol>\r\n \t<li>[latex]4x - 3 = 5[\/latex]<\/li>\r\n \t<li>[latex]12 - 5(x + 3) = 2x - 5[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{x}{3} - \\dfrac{3}{4} = \\dfrac{2x + 3}{12}[\/latex]<\/li>\r\n \t<li>[latex]3(2x - 1) + x = 5x + 3[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{x+2}{4} - \\dfrac{x-1}{3} = 2[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, solve each rational equation for [latex]x[\/latex]. State all [latex]x[\/latex]-values that are excluded from the solution set.\r\n<ol start=\"6\">\r\n \t<li>[latex]2 - \\dfrac{3}{x + 4} = \\dfrac{x + 2}{x + 4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{3x}{x - 1} + 2 = \\dfrac{3}{x - 1}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{x} = \\dfrac{1}{5} + \\dfrac{3}{2x}[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form.\r\n<ol start=\"9\">\r\n \t<li>[latex](1, 2)[\/latex] with a slope of [latex]-\\dfrac{4}{5}[\/latex]<\/li>\r\n \t<li>[latex]y[\/latex]-intercept is [latex]2[\/latex], and [latex](4, -1)[\/latex]<\/li>\r\n \t<li>[latex](1, 3)[\/latex] and [latex](5, 5)[\/latex]<\/li>\r\n \t<li>perpendicular to [latex]3y = x - 4[\/latex] and passes through the point [latex](-2, 1)[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, find the equation of the line using the given information.\r\n<ol start=\"13\">\r\n \t<li>[latex](1, 7)[\/latex] and [latex](3, 7)[\/latex]<\/li>\r\n \t<li>The slope equals zero and it passes through the point [latex](1, -4)[\/latex]<\/li>\r\n \t<li>[latex](-1, 3)[\/latex] and [latex](4, -5)[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.\r\n<ol start=\"16\">\r\n \t<li>[latex]3x - 2y = 5[\/latex] and [latex]6y - 9x = 6[\/latex]<\/li>\r\n \t<li>[latex]x = 4[\/latex] and [latex]y = -3[\/latex]<\/li>\r\n<\/ol>\r\n<h2><span data-sheets-root=\"1\">Modeling with Linear Equations<\/span><\/h2>\r\n<ol>\r\n \t<li>If the total amount of money you had to invest was [latex]$2,000[\/latex] and you deposit [latex]x[\/latex] amount in one investment, how can you represent the remaining amount?<\/li>\r\n \t<li>If Bill was traveling [latex]v[\/latex] mi\/h, how would you represent Daemon\u2019s speed if he was traveling [latex]10[\/latex] mi\/h faster?<\/li>\r\n<\/ol>\r\nFor the following exercise, use the information to find a linear algebraic equation model to use to answer the question being asked.\r\n<ol start=\"3\">\r\n \t<li>Beth and Ann are joking that their combined ages equal Sam\u2019s age. If Beth is twice Ann\u2019s age and Sam is [latex]69[\/latex] yr old, what are Beth and Ann\u2019s ages?<\/li>\r\n<\/ol>\r\nFor the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of [latex]$20[\/latex] and charges of [latex]$0.05[\/latex]\/min for calls. Company B has a monthly fee of [latex]$5[\/latex] and charges [latex]$0.10[\/latex]\/min for calls.\r\n<ol start=\"4\">\r\n \t<li>Find the model of the total cost of Company A\u2019s plan, using [latex]m[\/latex] for the minutes.<\/li>\r\n \t<li>Find the model of the total cost of Company B\u2019s plan, using [latex]m[\/latex] for the minutes.<\/li>\r\n \t<li>Find out how many minutes of calling would make the two plans equal.<\/li>\r\n \t<li>If the person makes a monthly average of [latex]200[\/latex] min of calls, which plan should for the person choose?<\/li>\r\n<\/ol>\r\nFor the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: [latex]$90[\/latex] monthly fee, unlimited talk and text on up to [latex]8[\/latex] lines, and data charges of [latex]$40[\/latex] for each device for up to [latex]2[\/latex] GB of data per device. The Mobile Share Plan: [latex]$120[\/latex] monthly fee for up to [latex]10[\/latex] devices, unlimited talk and text for all the lines, and data charges of [latex]$35[\/latex] for each device up to a shared [latex]total of [latex]10[\/latex] GB of data. Use [latex]P[\/latex] for the number of devices that need data plans as part of their cost.\r\n<ol start=\"8\">\r\n \t<li>Find the model of the total cost of the Family Plan.<\/li>\r\n \t<li>Find the model of the total cost of the Mobile Share Plan.<\/li>\r\n \t<li>Assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost.<\/li>\r\n \t<li>If a family has [latex]3[\/latex] smart phones, which plan should they choose?<\/li>\r\n<\/ol>\r\nFor exercises 12 and 13, use this scenario: A retired woman has [latex]50,000[\/latex] to invest but needs to make [latex]6,000[\/latex] a year from the interest to meet certain living expenses. One bond investment pays [latex]15\\%[\/latex] annual interest. The rest of it she wants to put in a CD that pays [latex]7\\%[\/latex].\r\n<ol start=\"12\">\r\n \t<li>If we let [latex]x[\/latex] be the amount the woman invests in the [latex]15\\%[\/latex] bond, how much will she be able to invest in the CD?<\/li>\r\n \t<li>Set up and solve the equation for how much the woman should invest in each option to sustain a [latex]6,000[\/latex] annual return.<\/li>\r\n \t<li>Two planes fly in opposite directions. One travels [latex]450 \\, \\text{mi\/h}[\/latex] and the other [latex]550 \\, \\text{mi\/h}[\/latex]. How long will it take before they are [latex]4{,}000 \\, \\text{mi}[\/latex] apart?<\/li>\r\n \t<li>Fiora starts riding her bike at [latex]20 \\, \\text{mi\/h}[\/latex]. After a while, she slows down to [latex]12 \\, \\text{mi\/h}[\/latex], and maintains that speed for the rest of the trip. The whole trip of [latex]70 \\, \\text{mi}[\/latex] takes her [latex]4.5 \\, \\text{h}[\/latex]. For what distance did she travel at [latex]20 \\, \\text{mi\/h}[\/latex]?<\/li>\r\n \t<li>Ra\u00fal has [latex]\\$20{,}000[\/latex] to invest. His intent is to earn [latex]11\\%[\/latex] interest on his investment. He can invest part of his money at [latex]8\\%[\/latex] interest and part at [latex]12\\%[\/latex] interest. How much does Ra\u00fal need to invest in each option to make a total [latex]11\\%[\/latex] return on his [latex]\\$20{,}000[\/latex]?<\/li>\r\n<\/ol>\r\nFor the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges [latex]$75\/\\text{wk}[\/latex] plus [latex]$0.10\/\\text{mi}[\/latex] driven. Plan B charges [latex]$100\/\\text{wk}[\/latex] plus [latex]$0.05\/\\text{mi}[\/latex] driven.\r\n<ol start=\"17\">\r\n \t<li>Write the model equation for the cost of renting a truck with plan A.<\/li>\r\n \t<li>Write the model equation for the cost of renting a truck with plan B.<\/li>\r\n \t<li>Find the number of miles that would generate the same cost for both plans.<\/li>\r\n \t<li>If Tim knows he has to travel [latex]300 \\, \\text{mi}[\/latex], which plan should he choose?<\/li>\r\n<\/ol>\r\nFor the following exercises, use the formula given to solve for the required value.\r\n<ol start=\"21\">\r\n \t<li>The formula [latex]F = \\dfrac{mv^2}{R}[\/latex] relates force ([latex]F[\/latex]), velocity ([latex]v[\/latex]), mass ([latex]m[\/latex]), and resistance ([latex]R[\/latex]). Find [latex]R[\/latex] when [latex]m = 45[\/latex], [latex]v = 7[\/latex], and [latex]F = 245[\/latex].<\/li>\r\n \t<li>[latex]\\text{Sum} = \\dfrac{1}{1 - r}[\/latex] is the formula for an infinite series sum. If the sum is [latex]5[\/latex], find [latex]r[\/latex].<\/li>\r\n<\/ol>\r\nFor the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.\r\n<ol start=\"23\">\r\n \t<li>Solve for [latex]W[\/latex]: [latex]P = 2L + 2W[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find the width, [latex]W[\/latex], of a rectangle whose length is [latex]15[\/latex] and whose perimeter is [latex]58[\/latex].<\/li>\r\n \t<li>Solve for [latex]f[\/latex]: [latex]\\dfrac{1}{p} + \\dfrac{1}{q} = \\dfrac{1}{f}[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find [latex]f[\/latex] when [latex]p = 8[\/latex] and [latex]q = 13[\/latex].<\/li>\r\n \t<li>Solve for [latex]m[\/latex] in the slope-intercept formula: [latex]y = mx + b[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find [latex]m[\/latex] when the coordinates of the point are ([latex]4[\/latex], [latex]7[\/latex]) and [latex]b = 12[\/latex].<\/li>\r\n \t<li>The area of a trapezoid is given by [latex]A = \\dfrac{1}{2} h (b_1 + b_2)[\/latex]. Use the formula to find the area of a trapezoid with [latex]h = 6[\/latex], [latex]b_1 = 14[\/latex], and [latex]b_2 = 8[\/latex].<\/li>\r\n \t<li>Solve for [latex]h[\/latex]: [latex]A = \\dfrac{1}{2} h (b_1 + b_2)[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find the height of a trapezoid with [latex]A = 150[\/latex], [latex]b_1 = 19[\/latex], and [latex]b_2 = 11[\/latex].<\/li>\r\n \t<li>Find the dimensions of an American football field. The length is [latex]200 \\, \\text{ft}[\/latex] more than the width, and the perimeter is [latex]1{,}040 \\, \\text{ft}[\/latex]. Find the length and width. Use the perimeter formula [latex]P = 2L + 2W[\/latex].<\/li>\r\n \t<li>Distance equals rate times time, [latex]d = rt[\/latex]. Find the distance Tom travels if he is moving at a rate of [latex]55 \\, \\text{mi\/h}[\/latex] for [latex]3.5 \\, \\text{h}[\/latex].<\/li>\r\n \t<li>Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of [latex]60 \\, \\text{mi\/h}[\/latex] for [latex]6.75 \\, \\text{h}[\/latex].<\/li>\r\n \t<li>Solve for [latex]h[\/latex]: [latex]A = \\dfrac{1}{2} b h[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find the height to the nearest tenth of a triangle with a base of [latex]15[\/latex] and an area of [latex]215[\/latex].<\/li>\r\n \t<li>The volume formula for a cylinder is [latex]V = \\pi r^2 h[\/latex]. Using the symbol [latex]\\pi[\/latex] in your answer, find the volume of a cylinder with a radius, [latex]r[\/latex], of [latex]4 \\, \\text{cm}[\/latex] and a height of [latex]14 \\, \\text{cm}[\/latex].<\/li>\r\n \t<li>Solve for [latex]h[\/latex]: [latex]V = \\pi r^2 h[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find the height of a cylinder with a radius of [latex]8[\/latex] and a volume of [latex]16\\pi[\/latex].<\/li>\r\n \t<li>Solve for [latex]r[\/latex]: [latex]V = \\pi r^2 h[\/latex]<\/li>\r\n \t<li>Use the formula from the previous question to find the radius of a cylinder with a height of [latex]36[\/latex] and a volume of [latex]324\\pi[\/latex].<\/li>\r\n \t<li>The formula for the circumference of a circle is [latex]C = 2 \\pi r[\/latex]. Find the circumference of a circle with a diameter of [latex]12 \\, \\text{in.}[\/latex] (diameter = [latex]2r[\/latex]). Use the symbol [latex]\\pi[\/latex] in your final answer.<\/li>\r\n \t<li>Solve the formula from the previous question for [latex]\\pi[\/latex]. Notice why [latex]\\pi[\/latex] is sometimes defined as the ratio of the circumference to its diameter.<\/li>\r\n<\/ol>\r\n<h2><span data-sheets-root=\"1\">Linear Inequalities<\/span><\/h2>\r\nFor the following exercises, solve the inequality. Write your final answer in interval notation.\r\n<ol>\r\n \t<li>[latex]3x + 2 \\geq 7x - 1[\/latex]<\/li>\r\n \t<li>[latex]4(x + 3) \\geq 2x - 1[\/latex]<\/li>\r\n \t<li>[latex]-5(x - 1) + 3 &gt; 3x - 4 - 4x[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{x + 3}{8} - \\dfrac{x + 5}{5} \\geq \\dfrac{3}{10}[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.\r\n<ol start=\"5\">\r\n \t<li>[latex]-4 &lt; 3x + 2 \\leq 18[\/latex]<\/li>\r\n \t<li>[latex]3x + 1 &gt; 2x - 5 &gt; x - 7[\/latex]<\/li>\r\n \t<li>[latex]3y &lt; 5 - 2y &lt; 7 + y[\/latex]<\/li>\r\n \t<li>[latex]2x - 5 \\leq -11 \\, \\text{or} \\, 5x + 1 \\geq 6[\/latex]<\/li>\r\n \t<li>[latex]x + 7 &lt; x + 2[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, write the set in interval notation.\r\n<ol start=\"10\">\r\n \t<li>[latex]\\{ x \\, | \\, -1 &lt; x &lt; 3 \\}[\/latex]<\/li>\r\n \t<li>[latex]\\{ x \\, | \\, x &lt; 4 \\}[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, write the interval in set-builder notation.\r\n<ol start=\"12\">\r\n \t<li>[latex](-\\infty, 6)[\/latex]<\/li>\r\n \t<li>[latex][-3, 5)[\/latex]<\/li>\r\n<\/ol>\r\nFor the following exercises, write the set of numbers represented on the number line in interval notation.\r\n<ol start=\"14\">\r\n \t<li>\r\n\r\n[caption id=\"attachment_6084\" align=\"alignnone\" width=\"300\"]<img class=\"wp-image-6084 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174659\/linear_inequalities_1-300x45.jpeg\" alt=\"\" width=\"300\" height=\"45\" \/> Number line with open circle at -2 and closed circle at -1[\/caption]<\/li>\r\n \t<li>\r\n\r\n[caption id=\"attachment_6085\" align=\"alignnone\" width=\"300\"]<img class=\"wp-image-6085 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174707\/linear_inequalities_2-300x43.jpeg\" alt=\"\" width=\"300\" height=\"43\" \/> Number line with closed circle at 4 and left-facing arrow[\/caption]<\/li>\r\n<\/ol>","rendered":"<h2><span data-sheets-root=\"1\">Graphing and Analyzing Linear Equations<\/span><\/h2>\n<p>For each of the following exercises, find the [latex]x[\/latex]-intercept and the [latex]y[\/latex]-intercept without graphing. Write the coordinates of each intercept.<\/p>\n<ol>\n<li>[latex]y = -3x + 6[\/latex]<\/li>\n<li>[latex]3x - 2y = 6[\/latex]<\/li>\n<li>[latex]3x + 8y = 9[\/latex]<\/li>\n<\/ol>\n<p>For each of the following exercises, solve the equation for [latex]y[\/latex] in terms of [latex]x[\/latex].<\/p>\n<ol start=\"4\">\n<li>[latex]4x + 2y = 8[\/latex]<\/li>\n<li>[latex]2x = 5 - 3y[\/latex]<\/li>\n<li>[latex]5y + 4 = 10x[\/latex]<\/li>\n<\/ol>\n<p>For each of the following exercises, find the distance between the two points. Simplify your answers, and write the exact answer in simplest radical form for irrational answers.<\/p>\n<ol start=\"7\">\n<li>[latex](-4, 1) \\text{ and } (3, -4)[\/latex]<\/li>\n<li>[latex](5, 0) \\text{ and } (5, 6)[\/latex]<\/li>\n<li>Find the distance between the two given points [latex](19, 12) \\text{ and } (41, 71)[\/latex] using your calculator, and round your answer to the nearest hundredth.<\/li>\n<\/ol>\n<p>For each of the following exercises, find the coordinates of the midpoint of the line segment that joins the two given points.<\/p>\n<ol start=\"10\">\n<li>[latex](-1, 1) \\text{ and } (7, -4)[\/latex]<\/li>\n<li>[latex](0, 7) \\text{ and } (4, -9)[\/latex]<\/li>\n<\/ol>\n<p>For each of the following exercises, identify the information requested.<\/p>\n<ol start=\"12\">\n<li>What are the coordinates of the origin?<\/li>\n<li>If a point is located on the y-axis, what is the x-coordinate?<\/li>\n<li>If a point is located on the x-axis, what is the y-coordinate?<\/li>\n<\/ol>\n<p>For each of the following exercises, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line).<\/p>\n<ol start=\"15\">\n<li>[latex](-1, 2), (0, 4), (2, 1)[\/latex]<br \/>\n<figure id=\"attachment_5226\" aria-describedby=\"caption-attachment-5226\" style=\"width: 288px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5226 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89-288x300.jpeg\" alt=\"\" width=\"288\" height=\"300\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89-288x300.jpeg 288w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89-65x68.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89-225x234.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89-350x365.jpeg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211108\/57c3f4cec52de848c03173fc88a600f371834e89.jpeg 357w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><figcaption id=\"caption-attachment-5226\" class=\"wp-caption-text\">Empty coordinate plane<\/figcaption><\/figure>\n<\/li>\n<li>Name the coordinates of the points graphed.<br \/>\n<figure id=\"attachment_5227\" aria-describedby=\"caption-attachment-5227\" style=\"width: 288px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5227 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8-288x300.jpeg\" alt=\"\" width=\"288\" height=\"300\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8-288x300.jpeg 288w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8-65x68.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8-225x234.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8-350x365.jpeg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211203\/ce1c14fcda83115e667a16b1c47eb96024d847c8.jpeg 357w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><figcaption id=\"caption-attachment-5227\" class=\"wp-caption-text\">Coordinate plane with points A,B,C<\/figcaption><\/figure>\n<\/li>\n<\/ol>\n<p>For each of the following exercises, construct a table and graph the equation by plotting at least three points.<\/p>\n<ol start=\"17\">\n<li>[latex]y = \\frac{1}{3}x + 2[\/latex]<\/li>\n<li>[latex]2y = x + 3[\/latex]<\/li>\n<\/ol>\n<p>For each of the following exercises, find and plot the [latex]x[\/latex]&#8211; and [latex]y[\/latex]-intercepts, and graph the straight line based on those two points.<\/p>\n<ol start=\"19\">\n<li>[latex]x - 2y = 8[\/latex]<\/li>\n<li>[latex]3y = -2x + 6[\/latex]<\/li>\n<\/ol>\n<figure id=\"attachment_5228\" aria-describedby=\"caption-attachment-5228\" style=\"width: 288px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5228 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad-288x300.jpeg\" alt=\"\" width=\"288\" height=\"300\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad-288x300.jpeg 288w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad-65x68.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad-225x234.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad-350x365.jpeg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/12211401\/b911e49676543a2d5545f53851220095d270b2ad.jpeg 357w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><figcaption id=\"caption-attachment-5228\" class=\"wp-caption-text\">Coordinate plane with line segment<\/figcaption><\/figure>\n<p>For each of the following exercises, use the graph in the figure below.<\/p>\n<ol start=\"21\">\n<li>Find the distance between the two endpoints using the distance formula. Round to three decimal places.<\/li>\n<li>Find the coordinates of the midpoint of the line segment connecting the two points.<\/li>\n<li>Find the distance that [latex](-3, 4)[\/latex] is from the origin.<\/li>\n<li>Find the distance that [latex](5, 2)[\/latex] is from the origin. Round to three decimal places.<\/li>\n<li>Which point is closer to the origin?<\/li>\n<\/ol>\n<p>For the following exercises, find the slope of the line that passes through the given points.<\/p>\n<ol start=\"26\">\n<li>[latex](5, 4)[\/latex] and [latex](7, 9)[\/latex]<\/li>\n<li>[latex](-3, 2)[\/latex] and [latex](4, -7)[\/latex]<\/li>\n<li>[latex](-5, 4)[\/latex] and [latex](2, 4)[\/latex]<\/li>\n<li>[latex](-1, -2)[\/latex] and [latex](3, 4)[\/latex]<\/li>\n<li>[latex](3, -2)[\/latex] and [latex](3, -2)[\/latex]<\/li>\n<\/ol>\n<h2><span data-sheets-root=\"1\">Equations of Lines<\/span><\/h2>\n<p>For the following exercises, solve the equation for [latex]x[\/latex].<\/p>\n<ol>\n<li>[latex]4x - 3 = 5[\/latex]<\/li>\n<li>[latex]12 - 5(x + 3) = 2x - 5[\/latex]<\/li>\n<li>[latex]\\dfrac{x}{3} - \\dfrac{3}{4} = \\dfrac{2x + 3}{12}[\/latex]<\/li>\n<li>[latex]3(2x - 1) + x = 5x + 3[\/latex]<\/li>\n<li>[latex]\\dfrac{x+2}{4} - \\dfrac{x-1}{3} = 2[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, solve each rational equation for [latex]x[\/latex]. State all [latex]x[\/latex]-values that are excluded from the solution set.<\/p>\n<ol start=\"6\">\n<li>[latex]2 - \\dfrac{3}{x + 4} = \\dfrac{x + 2}{x + 4}[\/latex]<\/li>\n<li>[latex]\\dfrac{3x}{x - 1} + 2 = \\dfrac{3}{x - 1}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{x} = \\dfrac{1}{5} + \\dfrac{3}{2x}[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form.<\/p>\n<ol start=\"9\">\n<li>[latex](1, 2)[\/latex] with a slope of [latex]-\\dfrac{4}{5}[\/latex]<\/li>\n<li>[latex]y[\/latex]-intercept is [latex]2[\/latex], and [latex](4, -1)[\/latex]<\/li>\n<li>[latex](1, 3)[\/latex] and [latex](5, 5)[\/latex]<\/li>\n<li>perpendicular to [latex]3y = x - 4[\/latex] and passes through the point [latex](-2, 1)[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, find the equation of the line using the given information.<\/p>\n<ol start=\"13\">\n<li>[latex](1, 7)[\/latex] and [latex](3, 7)[\/latex]<\/li>\n<li>The slope equals zero and it passes through the point [latex](1, -4)[\/latex]<\/li>\n<li>[latex](-1, 3)[\/latex] and [latex](4, -5)[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.<\/p>\n<ol start=\"16\">\n<li>[latex]3x - 2y = 5[\/latex] and [latex]6y - 9x = 6[\/latex]<\/li>\n<li>[latex]x = 4[\/latex] and [latex]y = -3[\/latex]<\/li>\n<\/ol>\n<h2><span data-sheets-root=\"1\">Modeling with Linear Equations<\/span><\/h2>\n<ol>\n<li>If the total amount of money you had to invest was [latex]$2,000[\/latex] and you deposit [latex]x[\/latex] amount in one investment, how can you represent the remaining amount?<\/li>\n<li>If Bill was traveling [latex]v[\/latex] mi\/h, how would you represent Daemon\u2019s speed if he was traveling [latex]10[\/latex] mi\/h faster?<\/li>\n<\/ol>\n<p>For the following exercise, use the information to find a linear algebraic equation model to use to answer the question being asked.<\/p>\n<ol start=\"3\">\n<li>Beth and Ann are joking that their combined ages equal Sam\u2019s age. If Beth is twice Ann\u2019s age and Sam is [latex]69[\/latex] yr old, what are Beth and Ann\u2019s ages?<\/li>\n<\/ol>\n<p>For the following exercises, use this scenario: Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of [latex]$20[\/latex] and charges of [latex]$0.05[\/latex]\/min for calls. Company B has a monthly fee of [latex]$5[\/latex] and charges [latex]$0.10[\/latex]\/min for calls.<\/p>\n<ol start=\"4\">\n<li>Find the model of the total cost of Company A\u2019s plan, using [latex]m[\/latex] for the minutes.<\/li>\n<li>Find the model of the total cost of Company B\u2019s plan, using [latex]m[\/latex] for the minutes.<\/li>\n<li>Find out how many minutes of calling would make the two plans equal.<\/li>\n<li>If the person makes a monthly average of [latex]200[\/latex] min of calls, which plan should for the person choose?<\/li>\n<\/ol>\n<p>For the following exercises, use this scenario: A wireless carrier offers the following plans that a person is considering. The Family Plan: [latex]$90[\/latex] monthly fee, unlimited talk and text on up to [latex]8[\/latex] lines, and data charges of [latex]$40[\/latex] for each device for up to [latex]2[\/latex] GB of data per device. The Mobile Share Plan: [latex]$120[\/latex] monthly fee for up to [latex]10[\/latex] devices, unlimited talk and text for all the lines, and data charges of [latex]$35[\/latex] for each device up to a shared [latex]total of [latex]10[\/latex] GB of data. Use [latex]P[\/latex] for the number of devices that need data plans as part of their cost.<\/p>\n<ol start=\"8\">\n<li>Find the model of the total cost of the Family Plan.<\/li>\n<li>Find the model of the total cost of the Mobile Share Plan.<\/li>\n<li>Assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost.<\/li>\n<li>If a family has [latex]3[\/latex] smart phones, which plan should they choose?<\/li>\n<\/ol>\n<p>For exercises 12 and 13, use this scenario: A retired woman has [latex]50,000[\/latex] to invest but needs to make [latex]6,000[\/latex] a year from the interest to meet certain living expenses. One bond investment pays [latex]15\\%[\/latex] annual interest. The rest of it she wants to put in a CD that pays [latex]7\\%[\/latex].<\/p>\n<ol start=\"12\">\n<li>If we let [latex]x[\/latex] be the amount the woman invests in the [latex]15\\%[\/latex] bond, how much will she be able to invest in the CD?<\/li>\n<li>Set up and solve the equation for how much the woman should invest in each option to sustain a [latex]6,000[\/latex] annual return.<\/li>\n<li>Two planes fly in opposite directions. One travels [latex]450 \\, \\text{mi\/h}[\/latex] and the other [latex]550 \\, \\text{mi\/h}[\/latex]. How long will it take before they are [latex]4{,}000 \\, \\text{mi}[\/latex] apart?<\/li>\n<li>Fiora starts riding her bike at [latex]20 \\, \\text{mi\/h}[\/latex]. After a while, she slows down to [latex]12 \\, \\text{mi\/h}[\/latex], and maintains that speed for the rest of the trip. The whole trip of [latex]70 \\, \\text{mi}[\/latex] takes her [latex]4.5 \\, \\text{h}[\/latex]. For what distance did she travel at [latex]20 \\, \\text{mi\/h}[\/latex]?<\/li>\n<li>Ra\u00fal has [latex]\\$20{,}000[\/latex] to invest. His intent is to earn [latex]11\\%[\/latex] interest on his investment. He can invest part of his money at [latex]8\\%[\/latex] interest and part at [latex]12\\%[\/latex] interest. How much does Ra\u00fal need to invest in each option to make a total [latex]11\\%[\/latex] return on his [latex]\\$20{,}000[\/latex]?<\/li>\n<\/ol>\n<p>For the following exercises, use this scenario: A truck rental agency offers two kinds of plans. Plan A charges [latex]$75\/\\text{wk}[\/latex] plus [latex]$0.10\/\\text{mi}[\/latex] driven. Plan B charges [latex]$100\/\\text{wk}[\/latex] plus [latex]$0.05\/\\text{mi}[\/latex] driven.<\/p>\n<ol start=\"17\">\n<li>Write the model equation for the cost of renting a truck with plan A.<\/li>\n<li>Write the model equation for the cost of renting a truck with plan B.<\/li>\n<li>Find the number of miles that would generate the same cost for both plans.<\/li>\n<li>If Tim knows he has to travel [latex]300 \\, \\text{mi}[\/latex], which plan should he choose?<\/li>\n<\/ol>\n<p>For the following exercises, use the formula given to solve for the required value.<\/p>\n<ol start=\"21\">\n<li>The formula [latex]F = \\dfrac{mv^2}{R}[\/latex] relates force ([latex]F[\/latex]), velocity ([latex]v[\/latex]), mass ([latex]m[\/latex]), and resistance ([latex]R[\/latex]). Find [latex]R[\/latex] when [latex]m = 45[\/latex], [latex]v = 7[\/latex], and [latex]F = 245[\/latex].<\/li>\n<li>[latex]\\text{Sum} = \\dfrac{1}{1 - r}[\/latex] is the formula for an infinite series sum. If the sum is [latex]5[\/latex], find [latex]r[\/latex].<\/li>\n<\/ol>\n<p>For the following exercises, solve for the given variable in the formula. After obtaining a new version of the formula, you will use it to solve a question.<\/p>\n<ol start=\"23\">\n<li>Solve for [latex]W[\/latex]: [latex]P = 2L + 2W[\/latex]<\/li>\n<li>Use the formula from the previous question to find the width, [latex]W[\/latex], of a rectangle whose length is [latex]15[\/latex] and whose perimeter is [latex]58[\/latex].<\/li>\n<li>Solve for [latex]f[\/latex]: [latex]\\dfrac{1}{p} + \\dfrac{1}{q} = \\dfrac{1}{f}[\/latex]<\/li>\n<li>Use the formula from the previous question to find [latex]f[\/latex] when [latex]p = 8[\/latex] and [latex]q = 13[\/latex].<\/li>\n<li>Solve for [latex]m[\/latex] in the slope-intercept formula: [latex]y = mx + b[\/latex]<\/li>\n<li>Use the formula from the previous question to find [latex]m[\/latex] when the coordinates of the point are ([latex]4[\/latex], [latex]7[\/latex]) and [latex]b = 12[\/latex].<\/li>\n<li>The area of a trapezoid is given by [latex]A = \\dfrac{1}{2} h (b_1 + b_2)[\/latex]. Use the formula to find the area of a trapezoid with [latex]h = 6[\/latex], [latex]b_1 = 14[\/latex], and [latex]b_2 = 8[\/latex].<\/li>\n<li>Solve for [latex]h[\/latex]: [latex]A = \\dfrac{1}{2} h (b_1 + b_2)[\/latex]<\/li>\n<li>Use the formula from the previous question to find the height of a trapezoid with [latex]A = 150[\/latex], [latex]b_1 = 19[\/latex], and [latex]b_2 = 11[\/latex].<\/li>\n<li>Find the dimensions of an American football field. The length is [latex]200 \\, \\text{ft}[\/latex] more than the width, and the perimeter is [latex]1{,}040 \\, \\text{ft}[\/latex]. Find the length and width. Use the perimeter formula [latex]P = 2L + 2W[\/latex].<\/li>\n<li>Distance equals rate times time, [latex]d = rt[\/latex]. Find the distance Tom travels if he is moving at a rate of [latex]55 \\, \\text{mi\/h}[\/latex] for [latex]3.5 \\, \\text{h}[\/latex].<\/li>\n<li>Using the formula in the previous exercise, find the distance that Susan travels if she is moving at a rate of [latex]60 \\, \\text{mi\/h}[\/latex] for [latex]6.75 \\, \\text{h}[\/latex].<\/li>\n<li>Solve for [latex]h[\/latex]: [latex]A = \\dfrac{1}{2} b h[\/latex]<\/li>\n<li>Use the formula from the previous question to find the height to the nearest tenth of a triangle with a base of [latex]15[\/latex] and an area of [latex]215[\/latex].<\/li>\n<li>The volume formula for a cylinder is [latex]V = \\pi r^2 h[\/latex]. Using the symbol [latex]\\pi[\/latex] in your answer, find the volume of a cylinder with a radius, [latex]r[\/latex], of [latex]4 \\, \\text{cm}[\/latex] and a height of [latex]14 \\, \\text{cm}[\/latex].<\/li>\n<li>Solve for [latex]h[\/latex]: [latex]V = \\pi r^2 h[\/latex]<\/li>\n<li>Use the formula from the previous question to find the height of a cylinder with a radius of [latex]8[\/latex] and a volume of [latex]16\\pi[\/latex].<\/li>\n<li>Solve for [latex]r[\/latex]: [latex]V = \\pi r^2 h[\/latex]<\/li>\n<li>Use the formula from the previous question to find the radius of a cylinder with a height of [latex]36[\/latex] and a volume of [latex]324\\pi[\/latex].<\/li>\n<li>The formula for the circumference of a circle is [latex]C = 2 \\pi r[\/latex]. Find the circumference of a circle with a diameter of [latex]12 \\, \\text{in.}[\/latex] (diameter = [latex]2r[\/latex]). Use the symbol [latex]\\pi[\/latex] in your final answer.<\/li>\n<li>Solve the formula from the previous question for [latex]\\pi[\/latex]. Notice why [latex]\\pi[\/latex] is sometimes defined as the ratio of the circumference to its diameter.<\/li>\n<\/ol>\n<h2><span data-sheets-root=\"1\">Linear Inequalities<\/span><\/h2>\n<p>For the following exercises, solve the inequality. Write your final answer in interval notation.<\/p>\n<ol>\n<li>[latex]3x + 2 \\geq 7x - 1[\/latex]<\/li>\n<li>[latex]4(x + 3) \\geq 2x - 1[\/latex]<\/li>\n<li>[latex]-5(x - 1) + 3 > 3x - 4 - 4x[\/latex]<\/li>\n<li>[latex]\\dfrac{x + 3}{8} - \\dfrac{x + 5}{5} \\geq \\dfrac{3}{10}[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.<\/p>\n<ol start=\"5\">\n<li>[latex]-4 < 3x + 2 \\leq 18[\/latex]<\/li>\n<li>[latex]3x + 1 > 2x - 5 > x - 7[\/latex]<\/li>\n<li>[latex]3y < 5 - 2y < 7 + y[\/latex]<\/li>\n<li>[latex]2x - 5 \\leq -11 \\, \\text{or} \\, 5x + 1 \\geq 6[\/latex]<\/li>\n<li>[latex]x + 7 < x + 2[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, write the set in interval notation.<\/p>\n<ol start=\"10\">\n<li>[latex]\\{ x \\, | \\, -1 < x < 3 \\}[\/latex]<\/li>\n<li>[latex]\\{ x \\, | \\, x < 4 \\}[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, write the interval in set-builder notation.<\/p>\n<ol start=\"12\">\n<li>[latex](-\\infty, 6)[\/latex]<\/li>\n<li>[latex][-3, 5)[\/latex]<\/li>\n<\/ol>\n<p>For the following exercises, write the set of numbers represented on the number line in interval notation.<\/p>\n<ol start=\"14\">\n<li>\n<figure id=\"attachment_6084\" aria-describedby=\"caption-attachment-6084\" style=\"width: 300px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6084 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174659\/linear_inequalities_1-300x45.jpeg\" alt=\"\" width=\"300\" height=\"45\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174659\/linear_inequalities_1-300x45.jpeg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174659\/linear_inequalities_1-65x10.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174659\/linear_inequalities_1-225x34.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174659\/linear_inequalities_1.jpeg 327w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-6084\" class=\"wp-caption-text\">Number line with open circle at -2 and closed circle at -1<\/figcaption><\/figure>\n<\/li>\n<li>\n<figure id=\"attachment_6085\" aria-describedby=\"caption-attachment-6085\" style=\"width: 300px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6085 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174707\/linear_inequalities_2-300x43.jpeg\" alt=\"\" width=\"300\" height=\"43\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174707\/linear_inequalities_2-300x43.jpeg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174707\/linear_inequalities_2-65x9.jpeg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174707\/linear_inequalities_2-225x32.jpeg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/09\/31174707\/linear_inequalities_2.jpeg 326w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><figcaption id=\"caption-attachment-6085\" class=\"wp-caption-text\">Number line with closed circle at 4 and left-facing arrow<\/figcaption><\/figure>\n<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":30,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":75,"module-header":"practice","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3434"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":19,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3434\/revisions"}],"predecessor-version":[{"id":7607,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3434\/revisions\/7607"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/75"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3434\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=3434"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=3434"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=3434"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=3434"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}