{"id":447,"date":"2015-10-26T18:49:10","date_gmt":"2015-10-26T18:49:10","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=447"},"modified":"2015-11-12T18:37:59","modified_gmt":"2015-11-12T18:37:59","slug":"solutions-to-selected-exercises-4","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/atd-sanjac-collegealgebra\/chapter\/solutions-to-selected-exercises-4\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]\\left[-3,5\\right][\/latex]\r\n\r\n2.\u00a0[latex]\\left(-\\infty ,-2\\right)\\cup \\left[3,\\infty \\right)[\/latex]\r\n\r\n3.\u00a0[latex]x<1[\/latex]\r\n\r\n4.\u00a0[latex]x\\ge -5[\/latex]\r\n\r\n5.\u00a0[latex]\\left(2,\\infty \\right)[\/latex]\r\n\r\n6.\u00a0[latex]\\left[-\\frac{3}{14},\\infty \\right)[\/latex]\r\n\r\n7.\u00a0[latex]6<x\\le 9\\text{ }\\text{ }\\text{or}\\left(6,9\\right][\/latex]\r\n\r\n8.\u00a0[latex]\\left(-\\frac{1}{8},\\frac{1}{2}\\right)[\/latex]\r\n\r\n9.\u00a0[latex]|x - 2|\\le 3[\/latex]\r\n\r\n10.\u00a0[latex]k\\le 1[\/latex] or [latex]k\\ge 7[\/latex]; in interval notation, this would be [latex]\\left(-\\infty ,1\\right]\\cup \\left[7,\\infty \\right)[\/latex].\r\n\"A\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.\r\n\r\n3.\u00a0[latex]\\left(-\\infty ,\\infty \\right)[\/latex]\r\n\r\n5.\u00a0We start by finding the x<\/em>-intercept, or where the function = 0. Once we have that point, which is [latex]\\left(3,0\\right)[\/latex], we graph to the right the straight line graph [latex]y=x - 3[\/latex], and then when we draw it to the left we plot positive y<\/em> values, taking the absolute value of them.\r\n\r\n7.\u00a0[latex]\\left(-\\infty ,\\frac{3}{4}\\right][\/latex]\r\n\r\n9.\u00a0[latex]\\left[\\frac{-13}{2},\\infty \\right)[\/latex]\r\n\r\n11.\u00a0[latex]\\left(-\\infty ,3\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(-\\infty ,-\\frac{37}{3}\\right][\/latex]\r\n\r\n15.\u00a0All real numbers [latex]\\left(-\\infty ,\\infty \\right)[\/latex]\r\n\r\n17.\u00a0[latex]\\left(-\\infty ,\\frac{-10}{3}\\right)\\cup \\left(4,\\infty \\right)[\/latex]\r\n\r\n19.\u00a0[latex]\\left(-\\infty ,-4\\right]\\cup \\left[8,+\\infty \\right)[\/latex]\r\n\r\n21.\u00a0No solution\r\n\r\n23.\u00a0[latex]\\left(-5,11\\right)[\/latex]\r\n\r\n25.\u00a0[latex]\\left[6,12\\right][\/latex]\r\n\r\n27.\u00a0[latex]\\left[-10,12\\right][\/latex]\r\n\r\n29.\u00a0[latex]\\begin{array}{ll}x> -6\\text{ and }x> -2\\hfill & \\text{Take the intersection of two sets}.\\hfill \\\\ x>-2,\\text{ }\\left(-2,+\\infty \\right)\\hfill & \\hfill \\end{array}[\/latex]\r\n\r\n31.\u00a0[latex]\\begin{array}{ll}x< -3\\text{ }\\mathrm{or}\\text{ }x\\ge 1\\hfill & \\text{Take the union of the two sets}.\\hfill \\\\ \\left(-\\infty ,-3\\right){\\cup }\\left[1,\\infty \\right)\\hfill & \\hfill \\end{array}[\/latex]\r\n\r\n33.\u00a0[latex]\\left(-\\infty ,-1\\right)\\cup \\left(3,\\infty \\right)[\/latex]\r\n\"A\r\n\r\n35.\u00a0[latex]\\left[-11,-3\\right][\/latex]\r\n\"A\r\n\r\n37.\u00a0It is never less than zero. No solution.\r\n\"A\r\n\r\n39.\u00a0Where the blue line is above the orange line; point of intersection is [latex]x=-3[\/latex].\r\n[latex]\\left(-\\infty ,-3\\right)[\/latex]\r\n\"A\r\n\r\n41.\u00a0Where the blue line is above the orange line; always. All real numbers.\r\n[latex]\\left(-\\infty ,-\\infty \\right)[\/latex]\r\n\"A\r\n\r\n43. [latex]\\left(-1,3\\right)[\/latex]\r\n\r\n45.\u00a0[latex]\\left(-\\infty ,4\\right)[\/latex]\r\n\r\n47.\u00a0[latex]\\{x|x<6\\}[\/latex]\r\n\r\n49.\u00a0[latex]\\{x|-3\\le x<5\\}[\/latex]\r\n\r\n51.\u00a0[latex]\\left(-2,1\\right][\/latex]\r\n\r\n53.\u00a0[latex]\\left(-\\infty ,4\\right][\/latex]\r\n\r\n55.\u00a0Where the blue is below the orange; always. All real numbers. [latex]\\left(-\\infty ,+\\infty \\right)[\/latex].\r\n\"A\r\n\r\n57.\u00a0Where the blue is below the orange; [latex]\\left(1,7\\right)[\/latex].\r\n\"A\r\n\r\n59.\u00a0[latex]x=2,\\frac{-4}{5}[\/latex]\r\n\r\n61.\u00a0[latex]\\left(-7,5\\right][\/latex]\r\n\r\n63.\u00a0[latex]\\begin{array}{l}80\\le T\\le 120\\\\ 1,600\\le 20T\\le 2,400\\end{array}[\/latex]\r\n[latex]\\left[1,600, 2,400\\right][\/latex]","rendered":"

Solutions to Try Its<\/h2>\n

1.\u00a0[latex]\\left[-3,5\\right][\/latex]<\/p>\n

2.\u00a0[latex]\\left(-\\infty ,-2\\right)\\cup \\left[3,\\infty \\right)[\/latex]<\/p>\n

3.\u00a0[latex]x<1[\/latex]\n\n4.\u00a0[latex]x\\ge -5[\/latex]\n\n5.\u00a0[latex]\\left(2,\\infty \\right)[\/latex]\n\n6.\u00a0[latex]\\left[-\\frac{3}{14},\\infty \\right)[\/latex]\n\n7.\u00a0[latex]6<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.<\/p>\n

3.\u00a0[latex]\\left(-\\infty ,\\infty \\right)[\/latex]<\/p>\n

5.\u00a0We start by finding the x<\/em>-intercept, or where the function = 0. Once we have that point, which is [latex]\\left(3,0\\right)[\/latex], we graph to the right the straight line graph [latex]y=x - 3[\/latex], and then when we draw it to the left we plot positive y<\/em> values, taking the absolute value of them.<\/p>\n

7.\u00a0[latex]\\left(-\\infty ,\\frac{3}{4}\\right][\/latex]<\/p>\n

9.\u00a0[latex]\\left[\\frac{-13}{2},\\infty \\right)[\/latex]<\/p>\n

11.\u00a0[latex]\\left(-\\infty ,3\\right)[\/latex]<\/p>\n

13.\u00a0[latex]\\left(-\\infty ,-\\frac{37}{3}\\right][\/latex]<\/p>\n

15.\u00a0All real numbers [latex]\\left(-\\infty ,\\infty \\right)[\/latex]<\/p>\n

17.\u00a0[latex]\\left(-\\infty ,\\frac{-10}{3}\\right)\\cup \\left(4,\\infty \\right)[\/latex]<\/p>\n

19.\u00a0[latex]\\left(-\\infty ,-4\\right]\\cup \\left[8,+\\infty \\right)[\/latex]<\/p>\n

21.\u00a0No solution<\/p>\n

23.\u00a0[latex]\\left(-5,11\\right)[\/latex]<\/p>\n

25.\u00a0[latex]\\left[6,12\\right][\/latex]<\/p>\n

27.\u00a0[latex]\\left[-10,12\\right][\/latex]<\/p>\n

29.\u00a0[latex]\\begin{array}{ll}x> -6\\text{ and }x> -2\\hfill & \\text{Take the intersection of two sets}.\\hfill \\\\ x>-2,\\text{ }\\left(-2,+\\infty \\right)\\hfill & \\hfill \\end{array}[\/latex]<\/p>\n

31.\u00a0[latex]\\begin{array}{ll}x< -3\\text{ }\\mathrm{or}\\text{ }x\\ge 1\\hfill & \\text{Take the union of the two sets}.\\hfill \\\\ \\left(-\\infty ,-3\\right){\\cup }\\left[1,\\infty \\right)\\hfill & \\hfill \\end{array}[\/latex]\n\n33.\u00a0[latex]\\left(-\\infty ,-1\\right)\\cup \\left(3,\\infty \\right)[\/latex]\n\"A<\/p>\n

35.\u00a0[latex]\\left[-11,-3\\right][\/latex]
\n\"A<\/p>\n

37.\u00a0It is never less than zero. No solution.
\n\"A<\/p>\n

39.\u00a0Where the blue line is above the orange line; point of intersection is [latex]x=-3[\/latex].
\n[latex]\\left(-\\infty ,-3\\right)[\/latex]
\n\"A<\/p>\n

41.\u00a0Where the blue line is above the orange line; always. All real numbers.
\n[latex]\\left(-\\infty ,-\\infty \\right)[\/latex]
\n\"A<\/p>\n

43. [latex]\\left(-1,3\\right)[\/latex]<\/p>\n

45.\u00a0[latex]\\left(-\\infty ,4\\right)[\/latex]<\/p>\n

47.\u00a0[latex]\\{x|x<6\\}[\/latex]\n\n49.\u00a0[latex]\\{x|-3\\le x<5\\}[\/latex]\n\n51.\u00a0[latex]\\left(-2,1\\right][\/latex]\n\n53.\u00a0[latex]\\left(-\\infty ,4\\right][\/latex]\n\n55.\u00a0Where the blue is below the orange; always. All real numbers. [latex]\\left(-\\infty ,+\\infty \\right)[\/latex].\n\"A<\/p>\n

57.\u00a0Where the blue is below the orange; [latex]\\left(1,7\\right)[\/latex].
\n\"A<\/p>\n

59.\u00a0[latex]x=2,\\frac{-4}{5}[\/latex]<\/p>\n

61.\u00a0[latex]\\left(-7,5\\right][\/latex]<\/p>\n

63.\u00a0[latex]\\begin{array}{l}80\\le T\\le 120\\\\ 1,600\\le 20T\\le 2,400\\end{array}[\/latex]
\n[latex]\\left[1,600, 2,400\\right][\/latex]<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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