{"id":967,"date":"2024-05-01T18:26:12","date_gmt":"2024-05-01T18:26:12","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=967"},"modified":"2025-08-21T23:07:33","modified_gmt":"2025-08-21T23:07:33","slug":"module-3-background-youll-need-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/module-3-background-youll-need-1\/","title":{"raw":"Linear Equations and Inequalities: Background You'll Need 1","rendered":"Linear Equations and Inequalities: Background You&#8217;ll Need 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Understand how to use a number line to place numbers and figure out which numbers are bigger or smaller using signs like [latex]&lt;[\/latex] and [latex]&gt;[\/latex]<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2 class=\"font-600 text-2xl font-bold\">Using Number Lines to Compare Numbers<\/h2>\r\n<p class=\"font-600 text-xl font-bold\">Number lines are powerful tools that help us visualize numbers and their relationships. They're especially useful for understanding which numbers are bigger or smaller, and for using comparison symbols like [latex]&lt;[\/latex] (less than) and [latex]&gt;[\/latex] (greater than).<\/p>\r\n\r\n<h3>Number Line<\/h3>\r\n<p class=\"whitespace-pre-wrap break-words\">A number line is a straight line where each point represents a number. Here are some key features:<\/p>\r\n\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">The line extends infinitely in both directions.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Numbers increase as you move right and decrease as you move left.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">The space between each whole number is divided into equal parts.<\/li>\r\n<\/ol>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>Number Line<\/h3>\r\nA <strong>number line<\/strong> is a visual representation of numbers on a straight line, typically drawn horizontally.\r\n\r\n&nbsp;\r\n\r\nEach point on the line corresponds to a number, with equal spacing between consecutive numbers, which allows for accurate measurement and comparison of the size of numbers.\r\n\r\n&nbsp;\r\n\r\nThe line includes a central point, typically marked as zero, with positive numbers extending infinitely to the right and negative numbers extending infinitely to the left.\r\n\r\n&nbsp;\r\n\r\n[caption id=\"attachment_1192\" align=\"aligncenter\" width=\"440\"]<img class=\"wp-image-1192 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006.png\" alt=\"\" width=\"440\" height=\"120\" \/> The number line with labels[\/caption]\r\n\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How to: Place Numbers on a Number Line<\/strong>\r\n<p class=\"whitespace-pre-wrap break-words\">To place a number on a number line:<\/p>\r\n\r\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Identify the nearest whole numbers.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Count the spaces between those whole numbers.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Place your number in the correct position between them.<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox example\">Plot the numbers on a number line: [latex]4, -3, -1.2 \\text{ and } \\frac{1}{2}[\/latex][reveal-answer q=\"984733\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"984733\"]\r\n<ul>\r\n \t<li>To plot [latex]4[\/latex], start at [latex]0[\/latex] and count four units to the right.<\/li>\r\n \t<li>To plot [latex]-3[\/latex], start at [latex]0[\/latex] and count three units to the left.<\/li>\r\n \t<li>To plot [latex]-1.2[\/latex], start at [latex]0[\/latex] and count one units to the left. From [latex]-1[\/latex], move slightly further left. Since [latex]-1.2[\/latex] is [latex]0.2[\/latex] units less than [latex]-1[\/latex], you move[latex]0.2[\/latex] units towards [latex]-2[\/latex]. The precise spot is [latex]20\\%[\/latex] of the way from [latex]-1[\/latex] to [latex]-2[\/latex].<\/li>\r\n \t<li>The number [latex]\\frac{1}{2}[\/latex] lies halfway between [latex]0[\/latex] and [latex]1[\/latex]. Identify the halfway mark and place the point there.<\/li>\r\n<\/ul>\r\n[caption id=\"attachment_1197\" align=\"aligncenter\" width=\"894\"]<img class=\"wp-image-1197 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM.png\" alt=\"\" width=\"894\" height=\"100\" \/> The number line with 4 points placed[\/caption]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18952[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18953[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18954[\/ohm2_question]<\/section>\r\n<h3 class=\"font-600 text-xl font-bold\">Comparing Numbers Using a Number Line<\/h3>\r\nWe can use the number line to compare and order positive and negative numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"440\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220114\/CNX_BMath_Figure_03_01_012.png\" alt=\"This figure is a number line. Above the number line there is an arrow pointing to the right labeled increasing. Below the number line there is an arrow pointing to the left labeled decreasing.\" width=\"440\" height=\"106\" \/> The number line with arrows indicating 'increasing' and 'decreasing'[\/caption]\r\n\r\nWe can use inequality symbols to show the ordering of positive and negative numbers.\r\n<ul>\r\n \t<li>[latex]a &lt; b [\/latex]: [latex]a[\/latex] is less than [latex]b[\/latex]\r\n<ul>\r\n \t<li>Use [latex]&lt;[\/latex] when the first number is to the left of the second number on the number line.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>[latex]a &gt; b [\/latex]: [latex]a[\/latex] is greater than [latex]b[\/latex]\r\n<ul>\r\n \t<li class=\"whitespace-normal break-words\">Use [latex]&gt;[\/latex] when the first number is to the right of the second number on the number line.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">\r\n<p class=\"whitespace-pre-wrap break-words\">The same principles apply to negative numbers, but remember:<\/p>\r\n\r\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\r\n \t<li class=\"whitespace-normal break-words\">Negative numbers are to the left of zero.<\/li>\r\n \t<li class=\"whitespace-normal break-words\">The more negative a number, the smaller it is.<\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox example\">Order each of the following pairs of numbers using [latex]&lt;[\/latex] or [latex]&gt;[\/latex].\r\n<ul>\r\n \t<li>[latex]14 \\text{ and }6[\/latex]<\/li>\r\n \t<li>[latex]-1 \\text{ and }9[\/latex]<\/li>\r\n \t<li>[latex]-1 \\text{ and }-4[\/latex]<\/li>\r\n \t<li>[latex]2 \\text{ and }-20[\/latex]<\/li>\r\n<\/ul>\r\n[reveal-answer q=\"395274\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"395274\"]\r\n\r\n[caption id=\"attachment_1200\" align=\"aligncenter\" width=\"745\"]<img class=\"wp-image-1200 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015.png\" alt=\"\" width=\"745\" height=\"65\" \/> Number line with points ordered[\/caption]\r\n<table id=\"eip-id1168469859124\" class=\"unnumbered unstyled\" style=\"width: 100%;\" summary=\".\"><\/table>\r\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1. Compare [latex]14[\/latex] and [latex]6[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]14[\/latex] is to the right of [latex]6[\/latex] on the number line.<\/td>\r\n<td>[latex]14&gt;6[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2. Compare [latex]-1[\/latex] and [latex]9[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-1[\/latex] is to the left of [latex]9[\/latex] on the number line.<\/td>\r\n<td>[latex]-1&lt;9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3. Compare [latex]-1[\/latex] and [latex]-4[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-1[\/latex] is to the right of [latex]-4[\/latex] on the number line.<\/td>\r\n<td>[latex]-1&gt;-4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>4. Compare [latex]2[\/latex] and [latex]-20[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2[\/latex] is to the right of [latex]-20[\/latex] on the number line.<\/td>\r\n<td>[latex]2&gt;-20[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]18955[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand how to use a number line to place numbers and figure out which numbers are bigger or smaller using signs like [latex]<[\/latex] and [latex]>[\/latex]<\/li>\n<\/ul>\n<\/section>\n<h2 class=\"font-600 text-2xl font-bold\">Using Number Lines to Compare Numbers<\/h2>\n<p class=\"font-600 text-xl font-bold\">Number lines are powerful tools that help us visualize numbers and their relationships. They&#8217;re especially useful for understanding which numbers are bigger or smaller, and for using comparison symbols like [latex]<[\/latex] (less than) and [latex]>[\/latex] (greater than).<\/p>\n<h3>Number Line<\/h3>\n<p class=\"whitespace-pre-wrap break-words\">A number line is a straight line where each point represents a number. Here are some key features:<\/p>\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">The line extends infinitely in both directions.<\/li>\n<li class=\"whitespace-normal break-words\">Numbers increase as you move right and decrease as you move left.<\/li>\n<li class=\"whitespace-normal break-words\">The space between each whole number is divided into equal parts.<\/li>\n<\/ol>\n<section class=\"textbox keyTakeaway\">\n<h3>Number Line<\/h3>\n<p>A <strong>number line<\/strong> is a visual representation of numbers on a straight line, typically drawn horizontally.<\/p>\n<p>&nbsp;<\/p>\n<p>Each point on the line corresponds to a number, with equal spacing between consecutive numbers, which allows for accurate measurement and comparison of the size of numbers.<\/p>\n<p>&nbsp;<\/p>\n<p>The line includes a central point, typically marked as zero, with positive numbers extending infinitely to the right and negative numbers extending infinitely to the left.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_1192\" aria-describedby=\"caption-attachment-1192\" style=\"width: 440px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1192 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006.png\" alt=\"\" width=\"440\" height=\"120\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006.png 440w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006-300x82.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006-65x18.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006-225x61.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/06233637\/CNX_BMath_Figure_03_01_006-350x95.png 350w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><figcaption id=\"caption-attachment-1192\" class=\"wp-caption-text\">The number line with labels<\/figcaption><\/figure>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How to: Place Numbers on a Number Line<\/strong><\/p>\n<p class=\"whitespace-pre-wrap break-words\">To place a number on a number line:<\/p>\n<ol class=\"-mt-1 list-decimal space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Identify the nearest whole numbers.<\/li>\n<li class=\"whitespace-normal break-words\">Count the spaces between those whole numbers.<\/li>\n<li class=\"whitespace-normal break-words\">Place your number in the correct position between them.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">Plot the numbers on a number line: [latex]4, -3, -1.2 \\text{ and } \\frac{1}{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q984733\">Show Answer<\/button><\/p>\n<div id=\"q984733\" class=\"hidden-answer\" style=\"display: none\">\n<ul>\n<li>To plot [latex]4[\/latex], start at [latex]0[\/latex] and count four units to the right.<\/li>\n<li>To plot [latex]-3[\/latex], start at [latex]0[\/latex] and count three units to the left.<\/li>\n<li>To plot [latex]-1.2[\/latex], start at [latex]0[\/latex] and count one units to the left. From [latex]-1[\/latex], move slightly further left. Since [latex]-1.2[\/latex] is [latex]0.2[\/latex] units less than [latex]-1[\/latex], you move[latex]0.2[\/latex] units towards [latex]-2[\/latex]. The precise spot is [latex]20\\%[\/latex] of the way from [latex]-1[\/latex] to [latex]-2[\/latex].<\/li>\n<li>The number [latex]\\frac{1}{2}[\/latex] lies halfway between [latex]0[\/latex] and [latex]1[\/latex]. Identify the halfway mark and place the point there.<\/li>\n<\/ul>\n<figure id=\"attachment_1197\" aria-describedby=\"caption-attachment-1197\" style=\"width: 894px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1197 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM.png\" alt=\"\" width=\"894\" height=\"100\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM.png 894w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM-300x34.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM-768x86.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM-65x7.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM-225x25.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07000103\/Screenshot-2024-05-06-at-5.00.58%E2%80%AFPM-350x39.png 350w\" sizes=\"(max-width: 894px) 100vw, 894px\" \/><figcaption id=\"caption-attachment-1197\" class=\"wp-caption-text\">The number line with 4 points placed<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18952\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18952&theme=lumen&iframe_resize_id=ohm18952&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18953\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18953&theme=lumen&iframe_resize_id=ohm18953&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm18954\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=18954&theme=lumen&iframe_resize_id=ohm18954&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3 class=\"font-600 text-xl font-bold\">Comparing Numbers Using a Number Line<\/h3>\n<p>We can use the number line to compare and order positive and negative numbers. Going from left to right, numbers increase in value. Going from right to left, numbers decrease in value.<\/p>\n<figure style=\"width: 440px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220114\/CNX_BMath_Figure_03_01_012.png\" alt=\"This figure is a number line. Above the number line there is an arrow pointing to the right labeled increasing. Below the number line there is an arrow pointing to the left labeled decreasing.\" width=\"440\" height=\"106\" \/><figcaption class=\"wp-caption-text\">The number line with arrows indicating &#8216;increasing&#8217; and &#8216;decreasing&#8217;<\/figcaption><\/figure>\n<p>We can use inequality symbols to show the ordering of positive and negative numbers.<\/p>\n<ul>\n<li>[latex]a < b[\/latex]: [latex]a[\/latex] is less than [latex]b[\/latex]\n\n\n<ul>\n<li>Use [latex]<[\/latex] when the first number is to the left of the second number on the number line.<\/li>\n<\/ul>\n<\/li>\n<li>[latex]a > b[\/latex]: [latex]a[\/latex] is greater than [latex]b[\/latex]\n<ul>\n<li class=\"whitespace-normal break-words\">Use [latex]>[\/latex] when the first number is to the right of the second number on the number line.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">\n<p class=\"whitespace-pre-wrap break-words\">The same principles apply to negative numbers, but remember:<\/p>\n<ul class=\"-mt-1 list-disc space-y-2 pl-8\">\n<li class=\"whitespace-normal break-words\">Negative numbers are to the left of zero.<\/li>\n<li class=\"whitespace-normal break-words\">The more negative a number, the smaller it is.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\">Order each of the following pairs of numbers using [latex]<[\/latex] or [latex]>[\/latex].<\/p>\n<ul>\n<li>[latex]14 \\text{ and }6[\/latex]<\/li>\n<li>[latex]-1 \\text{ and }9[\/latex]<\/li>\n<li>[latex]-1 \\text{ and }-4[\/latex]<\/li>\n<li>[latex]2 \\text{ and }-20[\/latex]<\/li>\n<\/ul>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q395274\">Show Answer<\/button><\/p>\n<div id=\"q395274\" class=\"hidden-answer\" style=\"display: none\">\n<figure id=\"attachment_1200\" aria-describedby=\"caption-attachment-1200\" style=\"width: 745px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1200 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015.png\" alt=\"\" width=\"745\" height=\"65\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015.png 745w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015-300x26.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015-65x6.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015-225x20.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/05\/07001311\/CNX_BMath_Figure_03_01_015-350x31.png 350w\" sizes=\"(max-width: 745px) 100vw, 745px\" \/><figcaption id=\"caption-attachment-1200\" class=\"wp-caption-text\">Number line with points ordered<\/figcaption><\/figure>\n<table id=\"eip-id1168469859124\" class=\"unnumbered unstyled\" style=\"width: 100%;\" summary=\".\"><\/table>\n<table id=\"eip-id1168468303840\" class=\"unnumbered unstyled\" style=\"font-family: 'Public Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\" summary=\".\">\n<tbody>\n<tr>\n<td>1. Compare [latex]14[\/latex] and [latex]6[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]14[\/latex] is to the right of [latex]6[\/latex] on the number line.<\/td>\n<td>[latex]14>6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2. Compare [latex]-1[\/latex] and [latex]9[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]-1[\/latex] is to the left of [latex]9[\/latex] on the number line.<\/td>\n<td>[latex]-1<9[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>3. Compare [latex]-1[\/latex] and [latex]-4[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>[latex]-1[\/latex] is to the right of [latex]-4[\/latex] on the number line.<\/td>\n<td>[latex]-1>-4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>4. 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