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3.5: Lin. Inequal. in One and Two Var.- Answers to the Homework Exercises

  • Page ID
    45042
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    Linear Inequalities

    1. \((-5,\infty )\)
    1. \((-\infty ,5]\)
    1. \((-\infty ,1]\)
    1. \(x<2;\: (-\infty ,2)\)
    1. \(x\geq 5;\: [5,\infty )\)
    1. \(x>-2;\: (-2,\infty )\)
    1. \([110,\infty )\)
      clipboard_e5789054a72b81e6a1d29e144d2c37707.png
    1. \([-6,\infty )\)
      clipboard_e3ea86170403626cce72535ff0130bab4.png
    1. \([11,\infty )\)
      clipboard_eecdcb1c306872395b0fb849578264bde.png
    1. \((-\infty ,-1)\)
      clipboard_e02731eb08cc0be5c41de5ae59572fa4f.png
    1. \((8,\infty )\)
      clipboard_e43ba1f4fd1d317af0ab21ce212639c46.png
    1. \((-\infty ,0)\)
      clipboard_e2639040c9359f6e3d93de17047edac3e.png
    1. \((-\infty ,\infty )\)
      clipboard_e59ad0203196c655697e85d33bd120041.png
    1. \((-\infty ,-6]\)
      clipboard_e9c6215cee23601a77e2804a3133459de.png
    1. \([1,\infty )\)
      clipboard_ee5176e2fdff68ffbdc37c7a3990591d8.png
    1. \((-\infty ,-10]\)
      clipboard_e74911f96858132c77f604ac1161da808.png
    1. \((-\infty ,5]\)
      clipboard_e5bb885832f5837518c597c9175c5302e.png
    1. \([0,\infty )\)
      clipboard_e2b30508ca5224462be779466711c3f55.png
    1. \((1,\infty )\)
      clipboard_e5e2d3ddda7202c94cfe636f51a1b7c5a.png
    1. \([-6,-2]\)
      clipboard_e6019a4b481c0fc6e19af0509f4bc59ef.png
    1. \((-2,2)\)
      clipboard_eb01e6bd0eb8361b228ae62e772efe8ee.png
    1. no solution
    1. \([-2,4]\)
      clipboard_e352902e2dcde3c9ced6e2c3d7e4ee498.png

    Compound Inequalities

    1. \(n ≤ −9\) or \(n ≥ 2\): \((−∞, −9] ∪ [2, ∞)\)
    1. \(x < −7:\: (−∞, −7)\)
    1. \(b < 5:\: (−∞, 5)\)
    1. \(−6 ≤ x ≤ −2 :\: [−6, −2]\)
    1. \(−2 < x < 2 :\: (−2, 2)\)
    1. No solution; \(∅\)
    1. \(5 ≤ x < 19 :\: [5, 19)\)
    1. \(k ≥ 2\) or \(k < −20:\: ( − ∞, −20) ∪ [2, ∞)\)
    1. \(m ≥ −4\) or \(m < −5 :\: (−∞, −5) ∪ [−4, ∞)\)
    1. \(n < −7\) or \(n > 8:\: ( − ∞ − 7), ∪(8, ∞)\)
    1. \(−2 ≤ n ≤ 6 :\: [−2, 6]\)
    1. \(−9 ≤ x ≤ 0 :\: [−9, 0]\)
    1. No solution; \(∅\)
    1. \(x ≤ 0\) or \(x > 8:\: ( − ∞, 0] ∪ (8, ∞)\)
    1. \(n < −14\) or \(n ≥ 17:\: ( − ∞, −14) ∪ [17, ∞)\)
    1. all real numbers

    Absolute Value Inequalities

    1. \(-3,\: 3\)
    1. \(-4,\:8\)
    1. \(-\frac{7}{3},\:\frac{11}{3}\)
    1. \(1,\:4\)
    1. \((−∞, −6) ∪ (0, ∞)\)
    1. \((−∞, −1] ∪ [3, ∞)\)
    1. \([1, 3]\)
    1. \(\left[ 1,\frac{3}{2}\right]\)
    1. \([2, 4]\)
    1. \(-8,\: 8\)
    1. \(-4,\: 20\)
    1. \(-7,\: 2\)
    1. \((−∞, 5) ∪ (5, ∞)\)
    1. \((−∞, −1) ∪ (5, ∞)\)
    1. \(\left[ -\frac{4}{3},2\right]\)
    1. \(\left[\frac{1}{2},1\right]\)
    1. \(\left[-2 ,-\frac{4}{3}\right]\)
    1. \([-3,-2]\)

    Linear Inequalities in Two Variables

    1. yes; no
    1. clipboard_e3569a03112ca60006ffcc43be908c434.png
      Figure \(\PageIndex{1}\)
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      Figure \(\PageIndex{2}\)
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      Figure \(\PageIndex{3}\)
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      Figure \(\PageIndex{4}\)
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      Figure \(\PageIndex{5}\)
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      Figure \(\PageIndex{6}\)

    This page titled 3.5: Lin. Inequal. in One and Two Var.- Answers to the Homework Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.