{"id":116,"date":"2026-01-12T15:48:44","date_gmt":"2026-01-12T15:48:44","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&p=116"},"modified":"2026-01-12T15:48:44","modified_gmt":"2026-01-12T15:48:44","slug":"linear-equations-and-inequalities-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/linear-equations-and-inequalities-get-stronger-answer-key\/","title":{"raw":"Linear Equations and Inequalities: Get Stronger Answer Key","rendered":"Linear Equations and Inequalities: Get Stronger Answer Key"},"content":{"raw":"

Graphing and Analyzing Linear Equations<\/span><\/h2>\r\n
    \r\n \t
  1. The x-intercept is [latex](2, 0)[\/latex] and the y-intercept is [latex](0, 6) [\/latex].<\/li>\r\n \t
  2. The x-intercept is [latex](2, 0)[\/latex] and the y-intercept is [latex](0, -3)[\/latex].<\/li>\r\n \t
  3. The x-intercept is [latex](3, 0)[\/latex] and the y-intercept is [latex](0, \\frac{9}{8})[\/latex].<\/li>\r\n \t
  4. [latex] y = 4 - 2x [\/latex]<\/li>\r\n \t
  5. [latex] y = \\frac{5 - 2x}{3} [\/latex]<\/li>\r\n \t
  6. [latex] y = 2x - \\frac{4}{5} [\/latex]<\/li>\r\n \t
  7. [latex] d = \\sqrt{74} [\/latex]<\/li>\r\n \t
  8. [latex] d = \\sqrt{36} = 6 [\/latex]<\/li>\r\n \t
  9. [latex] d \\approx 62.97 [\/latex]<\/li>\r\n \t
  10. [latex] \\left( 3, -\\frac{3}{2} \\right) [\/latex]<\/li>\r\n \t
  11. [latex] \\left( 2, -1 \\right) [\/latex]<\/li>\r\n \t
  12. [latex] (0, 0) [\/latex]<\/li>\r\n \t
  13. <\/li>\r\n \t
  14. [latex] y = 0 [\/latex]<\/li>\r\n \t
  15. \"\" not collinear<\/li>\r\n \t
  16. [latex] A: (-3, 2), B: (1, 3), C: (4, 0) [\/latex]<\/li>\r\n \t
  17. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/td>\r\n[latex]y[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]-3[\/latex]<\/td>\r\n[latex]1[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n[latex]2[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]3[\/latex]<\/td>\r\n[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]6[\/latex]<\/td>\r\n[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"\"<\/li>\r\n \t
  18. \r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]x[\/latex]<\/td>\r\n[latex]y[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]-3[\/latex]<\/td>\r\n[latex]0[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]0[\/latex]<\/td>\r\n[latex]1.5[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]3[\/latex]<\/td>\r\n[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"\"\"\"<\/li>\r\n \t
  19. \"\"<\/li>\r\n \t
  20. [latex] d = 8.246 [\/latex]<\/li>\r\n \t
  21. <\/li>\r\n \t
  22. [latex] d = 5 [\/latex]<\/li>\r\n \t
  23. <\/li>\r\n \t
  24. [latex] (-3, 4) [\/latex]<\/li>\r\n \t
  25. <\/li>\r\n \t
  26. [latex] m = -\\frac{9}{7} [\/latex]<\/li>\r\n \t
  27. <\/li>\r\n \t
  28. [latex] m = \\frac{3}{2} [\/latex]<\/li>\r\n \t
  29. <\/li>\r\n<\/ol>\r\n

    Equations of Lines<\/span><\/h2>\r\n
      \r\n \t
    1. [latex] x = 2 [\/latex]<\/li>\r\n \t
    2. [latex] x = \\frac{2}{7} [\/latex]<\/li>\r\n \t
    3. [latex] x = 6 [\/latex]<\/li>\r\n \t
    4. [latex] x = 3 [\/latex]<\/li>\r\n \t
    5. [latex] x = -14 [\/latex]<\/li>\r\n \t
    6. [latex] x \\neq -4; x = -3 [\/latex]<\/li>\r\n \t
    7. [latex] x \\neq 1; [\/latex] when we solve this we get [latex] x = 1 [\/latex], which is excluded, therefore NO solution<\/li>\r\n \t
    8. [latex] x \\neq 0; x = -\\frac{5}{2} [\/latex]<\/li>\r\n \t
    9. [latex] y = \\frac{4}{5}x + \\frac{14}{5} [\/latex]<\/li>\r\n \t
    10. [latex] y = \\frac{3}{4}x + 2 [\/latex]<\/li>\r\n \t
    11. [latex] y = \\frac{1}{2}x + \\frac{5}{2} [\/latex]<\/li>\r\n \t
    12. [latex] y = -3x - 5 [\/latex]<\/li>\r\n \t
    13. [latex] y = 7 [\/latex]<\/li>\r\n \t
    14. [latex] y = -4 [\/latex]<\/li>\r\n \t
    15. [latex] 8x + 5y = 7 [\/latex]<\/li>\r\n \t
    16. \"\"Parallel<\/li>\r\n \t
    17. \"\"Perpendicular<\/li>\r\n<\/ol>\r\n

      Modeling with Linear Equations<\/span><\/h2>\r\n
        \r\n \t
      1. [latex] 2,000 - x [\/latex]<\/li>\r\n \t
      2. [latex] v + 10 [\/latex]<\/li>\r\n \t
      3. [latex] \\text{Ann: } 23; \\text{Beth: } 46 [\/latex]<\/li>\r\n \t
      4. [latex] 20 + 0.05m [\/latex]<\/li>\r\n \t
      5. <\/li>\r\n \t
      6. [latex] 300 [\/latex] min<\/li>\r\n \t
      7. <\/li>\r\n \t
      8. [latex] 90 + 40P [\/latex]<\/li>\r\n \t
      9. <\/li>\r\n \t
      10. [latex] 6 [\/latex] devices<\/li>\r\n \t
      11. <\/li>\r\n \t
      12. [latex] 50,000 - x [\/latex]<\/li>\r\n \t
      13. <\/li>\r\n \t
      14. [latex] 4 [\/latex] h<\/li>\r\n \t
      15. She traveled for [latex] 2 [\/latex] hours at [latex] 20 [\/latex]mi\/h, or [latex] 40[\/latex] miles.<\/li>\r\n \t
      16. [latex] \\$5,000 \\text{ at 8% and } \\$15{,}000 \\text{ at 12%} [\/latex]<\/li>\r\n \t
      17. <\/li>\r\n \t
      18. [latex] B = 100 + 0.05x [\/latex]<\/li>\r\n \t
      19. <\/li>\r\n \t
      20. Plan A<\/li>\r\n \t
      21. [latex] R = 9 [\/latex]<\/li>\r\n \t
      22. [latex] r = \\frac{4}{5} \\text{ or } 0.8 [\/latex]<\/li>\r\n \t
      23. <\/li>\r\n \t
      24. [latex] W = \\frac{P - 2L}{2} = \\frac{58 - 2(15)}{2} = 14 [\/latex]<\/li>\r\n \t
      25. <\/li>\r\n \t
      26. [latex] f = \\frac{pq}{p + q} = \\frac{8(13)}{8 + 13} = \\frac{104}{21} [\/latex]<\/li>\r\n \t
      27. <\/li>\r\n \t
      28. [latex] m = - \\frac{5}{4} [\/latex]<\/li>\r\n \t
      29. <\/li>\r\n \t
      30. [latex] h = \\frac{2A}{b_1 + b_2} [\/latex]<\/li>\r\n \t
      31. <\/li>\r\n \t
      32. [latex] \\text{length} = 360 \\, \\text{ft}; \\, \\text{width} = 160 \\, \\text{ft} [\/latex]<\/li>\r\n \t
      33. <\/li>\r\n \t
      34. [latex] 405 \\, \\text{mi} [\/latex]<\/li>\r\n \t
      35. <\/li>\r\n \t
      36. [latex] 28.7 [\/latex]<\/li>\r\n \t
      37. <\/li>\r\n \t
      38. [latex] h = \\frac{V}{\\pi r^2} [\/latex]<\/li>\r\n \t
      39. <\/li>\r\n \t
      40. [latex] r = \\sqrt{\\frac{V}{\\pi h}} [\/latex]<\/li>\r\n \t
      41. <\/li>\r\n \t
      42. [latex] C = 12\\pi [\/latex]<\/li>\r\n \t
      43. <\/li>\r\n<\/ol>\r\n

        Linear Inequalities<\/span><\/h2>\r\n
          \r\n \t
        1. [latex] 14 + 7i [\/latex]<\/li>\r\n \t
        2. [latex] -\\frac{23}{29} + \\frac{15}{29}i [\/latex]<\/li>\r\n \t
        3. \"\"<\/li>\r\n \t
        4. \"\"<\/li>\r\n \t
        5. <\/li>\r\n \t
        6. [latex] 2 - \\frac{2}{3}i [\/latex]<\/li>\r\n \t
        7. <\/li>\r\n \t
        8. [latex] 4 - 6i [\/latex]<\/li>\r\n \t
        9. <\/li>\r\n \t
        10. [latex] 128i [\/latex]<\/li>\r\n \t
        11. [latex] \\left( \\frac{\\sqrt{3}}{2} + \\frac{1}{2}i \\right)^6 = -1 [\/latex]<\/li>\r\n \t
        12. [latex] 3i [\/latex]<\/li>\r\n \t
        13. [latex] 0 [\/latex]<\/li>\r\n \t
        14. [latex] 5 - 5i [\/latex]<\/li>\r\n \t
        15. [latex] -2i [\/latex]<\/li>\r\n<\/ol>","rendered":"

          Graphing and Analyzing Linear Equations<\/span><\/h2>\n
            \n
          1. The x-intercept is [latex](2, 0)[\/latex] and the y-intercept is [latex](0, 6)[\/latex].<\/li>\n
          2. The x-intercept is [latex](2, 0)[\/latex] and the y-intercept is [latex](0, -3)[\/latex].<\/li>\n
          3. The x-intercept is [latex](3, 0)[\/latex] and the y-intercept is [latex](0, \\frac{9}{8})[\/latex].<\/li>\n
          4. [latex]y = 4 - 2x[\/latex]<\/li>\n
          5. [latex]y = \\frac{5 - 2x}{3}[\/latex]<\/li>\n
          6. [latex]y = 2x - \\frac{4}{5}[\/latex]<\/li>\n
          7. [latex]d = \\sqrt{74}[\/latex]<\/li>\n
          8. [latex]d = \\sqrt{36} = 6[\/latex]<\/li>\n
          9. [latex]d \\approx 62.97[\/latex]<\/li>\n
          10. [latex]\\left( 3, -\\frac{3}{2} \\right)[\/latex]<\/li>\n
          11. [latex]\\left( 2, -1 \\right)[\/latex]<\/li>\n
          12. [latex](0, 0)[\/latex]<\/li>\n
          13. <\/li>\n
          14. [latex]y = 0[\/latex]<\/li>\n
          15. \"\" not collinear<\/li>\n
          16. [latex]A: (-3, 2), B: (1, 3), C: (4, 0)[\/latex]<\/li>\n
          17. \n\n\n\n\n\n\n\n
            [latex]x[\/latex]<\/td>\n[latex]y[\/latex]<\/td>\n<\/tr>\n
            [latex]-3[\/latex]<\/td>\n[latex]1[\/latex]<\/td>\n<\/tr>\n
            [latex]0[\/latex]<\/td>\n[latex]2[\/latex]<\/td>\n<\/tr>\n
            [latex]3[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n<\/tr>\n
            [latex]6[\/latex]<\/td>\n[latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            \"\"<\/li>\n

          18. \n\n\n\n\n\n\n
            [latex]x[\/latex]<\/td>\n[latex]y[\/latex]<\/td>\n<\/tr>\n
            [latex]-3[\/latex]<\/td>\n[latex]0[\/latex]<\/td>\n<\/tr>\n
            [latex]0[\/latex]<\/td>\n[latex]1.5[\/latex]<\/td>\n<\/tr>\n
            [latex]3[\/latex]<\/td>\n[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            \"\"\"\"<\/li>\n

          19. \"\"<\/li>\n
          20. [latex]d = 8.246[\/latex]<\/li>\n
          21. <\/li>\n
          22. [latex]d = 5[\/latex]<\/li>\n
          23. <\/li>\n
          24. [latex](-3, 4)[\/latex]<\/li>\n
          25. <\/li>\n
          26. [latex]m = -\\frac{9}{7}[\/latex]<\/li>\n
          27. <\/li>\n
          28. [latex]m = \\frac{3}{2}[\/latex]<\/li>\n
          29. <\/li>\n<\/ol>\n

            Equations of Lines<\/span><\/h2>\n
              \n
            1. [latex]x = 2[\/latex]<\/li>\n
            2. [latex]x = \\frac{2}{7}[\/latex]<\/li>\n
            3. [latex]x = 6[\/latex]<\/li>\n
            4. [latex]x = 3[\/latex]<\/li>\n
            5. [latex]x = -14[\/latex]<\/li>\n
            6. [latex]x \\neq -4; x = -3[\/latex]<\/li>\n
            7. [latex]x \\neq 1;[\/latex] when we solve this we get [latex]x = 1[\/latex], which is excluded, therefore NO solution<\/li>\n
            8. [latex]x \\neq 0; x = -\\frac{5}{2}[\/latex]<\/li>\n
            9. [latex]y = \\frac{4}{5}x + \\frac{14}{5}[\/latex]<\/li>\n
            10. [latex]y = \\frac{3}{4}x + 2[\/latex]<\/li>\n
            11. [latex]y = \\frac{1}{2}x + \\frac{5}{2}[\/latex]<\/li>\n
            12. [latex]y = -3x - 5[\/latex]<\/li>\n
            13. [latex]y = 7[\/latex]<\/li>\n
            14. [latex]y = -4[\/latex]<\/li>\n
            15. [latex]8x + 5y = 7[\/latex]<\/li>\n
            16. \"\"Parallel<\/li>\n
            17. \"\"Perpendicular<\/li>\n<\/ol>\n

              Modeling with Linear Equations<\/span><\/h2>\n
                \n
              1. [latex]2,000 - x[\/latex]<\/li>\n
              2. [latex]v + 10[\/latex]<\/li>\n
              3. [latex]\\text{Ann: } 23; \\text{Beth: } 46[\/latex]<\/li>\n
              4. [latex]20 + 0.05m[\/latex]<\/li>\n
              5. <\/li>\n
              6. [latex]300[\/latex] min<\/li>\n
              7. <\/li>\n
              8. [latex]90 + 40P[\/latex]<\/li>\n
              9. <\/li>\n
              10. [latex]6[\/latex] devices<\/li>\n
              11. <\/li>\n
              12. [latex]50,000 - x[\/latex]<\/li>\n
              13. <\/li>\n
              14. [latex]4[\/latex] h<\/li>\n
              15. She traveled for [latex]2[\/latex] hours at [latex]20[\/latex]mi\/h, or [latex]40[\/latex] miles.<\/li>\n
              16. [latex]\\$5,000 \\text{ at 8% and } \\$15{,}000 \\text{ at 12%}[\/latex]<\/li>\n
              17. <\/li>\n
              18. [latex]B = 100 + 0.05x[\/latex]<\/li>\n
              19. <\/li>\n
              20. Plan A<\/li>\n
              21. [latex]R = 9[\/latex]<\/li>\n
              22. [latex]r = \\frac{4}{5} \\text{ or } 0.8[\/latex]<\/li>\n
              23. <\/li>\n
              24. [latex]W = \\frac{P - 2L}{2} = \\frac{58 - 2(15)}{2} = 14[\/latex]<\/li>\n
              25. <\/li>\n
              26. [latex]f = \\frac{pq}{p + q} = \\frac{8(13)}{8 + 13} = \\frac{104}{21}[\/latex]<\/li>\n
              27. <\/li>\n
              28. [latex]m = - \\frac{5}{4}[\/latex]<\/li>\n
              29. <\/li>\n
              30. [latex]h = \\frac{2A}{b_1 + b_2}[\/latex]<\/li>\n
              31. <\/li>\n
              32. [latex]\\text{length} = 360 \\, \\text{ft}; \\, \\text{width} = 160 \\, \\text{ft}[\/latex]<\/li>\n
              33. <\/li>\n
              34. [latex]405 \\, \\text{mi}[\/latex]<\/li>\n
              35. <\/li>\n
              36. [latex]28.7[\/latex]<\/li>\n
              37. <\/li>\n
              38. [latex]h = \\frac{V}{\\pi r^2}[\/latex]<\/li>\n
              39. <\/li>\n
              40. [latex]r = \\sqrt{\\frac{V}{\\pi h}}[\/latex]<\/li>\n
              41. <\/li>\n
              42. [latex]C = 12\\pi[\/latex]<\/li>\n
              43. <\/li>\n<\/ol>\n

                Linear Inequalities<\/span><\/h2>\n
                  \n
                1. [latex]14 + 7i[\/latex]<\/li>\n
                2. [latex]-\\frac{23}{29} + \\frac{15}{29}i[\/latex]<\/li>\n
                3. \"\"<\/li>\n
                4. \"\"<\/li>\n
                5. <\/li>\n
                6. [latex]2 - \\frac{2}{3}i[\/latex]<\/li>\n
                7. <\/li>\n
                8. [latex]4 - 6i[\/latex]<\/li>\n
                9. <\/li>\n
                10. [latex]128i[\/latex]<\/li>\n
                11. [latex]\\left( \\frac{\\sqrt{3}}{2} + \\frac{1}{2}i \\right)^6 = -1[\/latex]<\/li>\n
                12. [latex]3i[\/latex]<\/li>\n
                13. [latex]0[\/latex]<\/li>\n
                14. [latex]5 - 5i[\/latex]<\/li>\n
                15. [latex]-2i[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":106,"module-header":"- Select Header -","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\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/116"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":1,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/116\/revisions"}],"predecessor-version":[{"id":124,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/116\/revisions\/124"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/106"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/116\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=116"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=116"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=116"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}