{"id":445,"date":"2015-10-26T18:47:45","date_gmt":"2015-10-26T18:47:45","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=445"},"modified":"2015-11-12T18:37:59","modified_gmt":"2015-11-12T18:37:59","slug":"section-exercises-12","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/section-exercises-12\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"1.\u00a0When solving an inequality, explain what happened from Step 1 to Step 2:\r\n
[latex]\\begin{array}{ll}\\text{Step 1}\\hfill & -2x>6\\hfill \\\\ \\text{Step 2}\\hfill & x<-3\\hfill \\end{array}[\/latex]<\/div>\r\n2.\u00a0When solving an inequality, we arrive at\r\n
[latex]\\begin{array}{l}x+2< x+3\\hfill \\\\ 2< 3\\hfill \\end{array}[\/latex]<\/div>\r\nExplain what our solution set is.\r\n\r\n3. When writing our solution in interval notation, how do we represent all the real numbers?\r\n\r\n4.\u00a0When solving an inequality, we arrive at\r\n
[latex]\\begin{array}{l}x+2>x+3\\hfill \\\\ 2>3\\hfill \\end{array}[\/latex]<\/div>\r\nExplain what our solution set is.\r\n\r\n5. Describe how to graph [latex]y=|x - 3|[\/latex]\r\n\r\nFor the following exercises, solve the inequality. Write your final answer in interval notation.\r\n\r\n6. [latex]4x - 7\\le 9[\/latex]\r\n\r\n7. [latex]3x+2\\ge 7x - 1[\/latex]\r\n\r\n8.\u00a0[latex]-2x+3>x - 5[\/latex]\r\n\r\n9. [latex]4\\left(x+3\\right)\\ge 2x - 1[\/latex]\r\n\r\n10.\u00a0[latex]-\\frac{1}{2}x\\le \\frac{-5}{4}+\\frac{2}{5}x[\/latex]\r\n\r\n11. [latex]-5\\left(x - 1\\right)+3>3x - 4-4x[\/latex]\r\n\r\n12.\u00a0[latex]-3\\left(2x+1\\right)>-2\\left(x+4\\right)[\/latex]\r\n\r\n13. [latex]\\frac{x+3}{8}-\\frac{x+5}{5}\\ge \\frac{3}{10}[\/latex]\r\n\r\n14.\u00a0[latex]\\frac{x - 1}{3}+\\frac{x+2}{5}\\le \\frac{3}{5}[\/latex]\r\n\r\nFor the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation.\r\n\r\n15. [latex]|x+9|\\ge -6[\/latex]\r\n\r\n16.\u00a0[latex]|2x+3|<7[\/latex]\r\n\r\n17. [latex]|3x - 1|>11[\/latex]\r\n\r\n18.\u00a0[latex]|2x+1|+1\\le 6[\/latex]\r\n\r\n19. [latex]|x - 2|+4\\ge 10[\/latex]\r\n\r\n20.\u00a0[latex]|-2x+7|\\le 13[\/latex]\r\n\r\n21. [latex]|x - 7|<-4[\/latex]\r\n\r\n22.\u00a0[latex]|x - 20|>-1[\/latex]\r\n\r\n23. [latex]|\\frac{x - 3}{4}|<2[\/latex]\r\n\r\nFor the following exercises, describe all the x<\/em>-values within or including a distance of the given values.\r\n\r\n24. Distance of 5 units from the number 7\r\n\r\n25. Distance of 3 units from the number 9\r\n\r\n26.\u00a0Distance of 10 units from the number 4\r\n\r\n27. Distance of 11 units from the number 1\r\n\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\r\n28. [latex]-4<3x+2\\le 18[\/latex]\r\n\r\n29. [latex]3x+1>2x - 5>x - 7[\/latex]\r\n\r\n30.\u00a0[latex]3y<5 - 2y<7+y[\/latex]\r\n\r\n31. [latex]2x - 5<-11\\text{ or }5x+1\\ge 6[\/latex]\r\n\r\n32.\u00a0[latex]x+7<x+2[\/latex]\r\n\r\nFor the following exercises, graph the function. Observe the points of intersection and shade the x<\/em>-axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.\r\n\r\n33. [latex]|x - 1|>2[\/latex]\r\n\r\n34. [latex]|x+3|\\ge 5[\/latex]\r\n\r\n35. [latex]|x+7|\\le 4[\/latex]\r\n\r\n36. [latex]|x - 2|<7[\/latex]\r\n\r\n37. [latex]|x - 2|<0[\/latex]\r\n\r\nFor the following exercises, graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y<\/em>-values of the lines.\r\n\r\n38. [latex]x+3<3x - 4[\/latex]\r\n\r\n39. [latex]x - 2>2x+1[\/latex]\r\n\r\n40. [latex]x+1>x+4[\/latex]\r\n\r\n41. [latex]\\frac{1}{2}x+1>\\frac{1}{2}x - 5[\/latex]\r\n\r\n42. [latex]4x+1<\\frac{1}{2}x+3[\/latex]\r\n\r\nFor the following exercises, write the set in interval notation.\r\n\r\n43. [latex]\\{x|-1<x<3\\}[\/latex]\r\n\r\n44.\u00a0[latex]\\{x|x\\ge 7\\}[\/latex]\r\n\r\n45. [latex]\\{x|x<4\\}[\/latex]\r\n\r\n46.\u00a0[latex]\\{x|x\\text{ is all real numbers}\\}[\/latex]\r\n\r\nFor the following exercises, write the interval in set-builder notation.\r\n\r\n47. [latex]\\left(-\\infty ,6\\right)[\/latex]\r\n\r\n48.\u00a0[latex]\\left(4,+\\infty \\right)[\/latex]\r\n\r\n49. [latex]\\left[-3,5\\right)[\/latex]\r\n\r\n50. [latex]\\left[-4,1\\right]\\cup \\left[9,\\infty \\right)[\/latex]\r\n\r\nFor the following exercises, write the set of numbers represented on the number line in interval notation.\r\n\r\n51.\r\n\"A\r\n\r\n52.\r\n\"Number\r\n\r\n53.\r\n\"Number\r\n\r\nFor the following exercises, input the left-hand side of the inequality as a Y1 graph in your graphing utility. Enter y2 = the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, 1:abs(. Find the points of intersection, recall (2nd<\/sup> CALC 5:intersection, 1st<\/sup> curve, enter, 2nd<\/sup> curve, enter, guess, enter). Copy a sketch of the graph and shade the x<\/em>-axis for your solution set to the inequality. Write final answers in interval notation.\r\n\r\n54. [latex]|x+2|-5< 2[\/latex]\r\n\r\n55. [latex]\\frac{-1}{2}|x+2|< 4[\/latex]\r\n\r\n56. [latex]|4x+1|-3> 2[\/latex]\r\n\r\n57. [latex]|x - 4|< 3[\/latex]\r\n\r\n58. [latex]|x+2|\\ge 5[\/latex]\r\n\r\n59.\u00a0Solve [latex]|3x+1|=|2x+3|[\/latex]\r\n\r\n60.\u00a0Solve [latex]{x}^{2}-x>12[\/latex]\r\n\r\n61. [latex]\\frac{x - 5}{x+7}\\le 0[\/latex], [latex]x\\ne -7[\/latex]\r\n\r\n62.\u00a0[latex]p=-{x}^{2}+130x - 3000[\/latex] is a profit formula for a small business. Find the set of x<\/em>-values that will keep this profit positive.\r\n\r\n63.\u00a0In chemistry the volume for a certain gas is given by [latex]V=20T[\/latex], where V<\/em> is measured in cc and T<\/em> is temperature in \u00baC. If the temperature varies between 80\u00baC and 120\u00baC, find the set of volume values.\r\n\r\n64.\u00a0A basic cellular package costs $20\/mo. for 60 min of calling, with an additional charge of $.30\/min beyond that time. The cost formula would be [latex]C=\\$20+.30\\left(x - 60\\right)[\/latex]. If you have to keep your bill lower than $50, what is the maximum calling minutes you can use?\r\n

<\/h1>","rendered":"

1.\u00a0When solving an inequality, explain what happened from Step 1 to Step 2:<\/p>\n

[latex]\\begin{array}{ll}\\text{Step 1}\\hfill & -2x>6\\hfill \\\\ \\text{Step 2}\\hfill & x<-3\\hfill \\end{array}[\/latex]<\/div>\n

2.\u00a0When solving an inequality, we arrive at<\/p>\n

[latex]\\begin{array}{l}x+2< x+3\\hfill \\\\ 2< 3\\hfill \\end{array}[\/latex]<\/div>\n

Explain what our solution set is.<\/p>\n

3. When writing our solution in interval notation, how do we represent all the real numbers?<\/p>\n

4.\u00a0When solving an inequality, we arrive at<\/p>\n

[latex]\\begin{array}{l}x+2>x+3\\hfill \\\\ 2>3\\hfill \\end{array}[\/latex]<\/div>\n

Explain what our solution set is.<\/p>\n

5. Describe how to graph [latex]y=|x - 3|[\/latex]<\/p>\n

For the following exercises, solve the inequality. Write your final answer in interval notation.<\/p>\n

6. [latex]4x - 7\\le 9[\/latex]<\/p>\n

7. [latex]3x+2\\ge 7x - 1[\/latex]<\/p>\n

8.\u00a0[latex]-2x+3>x - 5[\/latex]<\/p>\n

9. [latex]4\\left(x+3\\right)\\ge 2x - 1[\/latex]<\/p>\n

10.\u00a0[latex]-\\frac{1}{2}x\\le \\frac{-5}{4}+\\frac{2}{5}x[\/latex]<\/p>\n

11. [latex]-5\\left(x - 1\\right)+3>3x - 4-4x[\/latex]<\/p>\n

12.\u00a0[latex]-3\\left(2x+1\\right)>-2\\left(x+4\\right)[\/latex]<\/p>\n

13. [latex]\\frac{x+3}{8}-\\frac{x+5}{5}\\ge \\frac{3}{10}[\/latex]<\/p>\n

14.\u00a0[latex]\\frac{x - 1}{3}+\\frac{x+2}{5}\\le \\frac{3}{5}[\/latex]<\/p>\n

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation.<\/p>\n

15. [latex]|x+9|\\ge -6[\/latex]<\/p>\n

16.\u00a0[latex]|2x+3|<7[\/latex]\n\n17. [latex]|3x - 1|>11[\/latex]<\/p>\n

18.\u00a0[latex]|2x+1|+1\\le 6[\/latex]<\/p>\n

19. [latex]|x - 2|+4\\ge 10[\/latex]<\/p>\n

20.\u00a0[latex]|-2x+7|\\le 13[\/latex]<\/p>\n

21. [latex]|x - 7|<-4[\/latex]\n\n22.\u00a0[latex]|x - 20|>-1[\/latex]<\/p>\n

23. [latex]|\\frac{x - 3}{4}|<2[\/latex]\n\nFor the following exercises, describe all the x<\/em>-values within or including a distance of the given values.<\/p>\n

24. Distance of 5 units from the number 7<\/p>\n

25. Distance of 3 units from the number 9<\/p>\n

26.\u00a0Distance of 10 units from the number 4<\/p>\n

27. Distance of 11 units from the number 1<\/p>\n

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.<\/p>\n

28. [latex]-4<3x+2\\le 18[\/latex]\n\n29. [latex]3x+1>2x - 5>x - 7[\/latex]<\/p>\n

30.\u00a0[latex]3y<5 - 2y<7+y[\/latex]\n\n31. [latex]2x - 5<-11\\text{ or }5x+1\\ge 6[\/latex]\n\n32.\u00a0[latex]x+7x<\/em>-axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.<\/p>\n

33. [latex]|x - 1|>2[\/latex]<\/p>\n

34. [latex]|x+3|\\ge 5[\/latex]<\/p>\n

35. [latex]|x+7|\\le 4[\/latex]<\/p>\n

36. [latex]|x - 2|<7[\/latex]\n\n37. [latex]|x - 2|<0[\/latex]\n\nFor the following exercises, graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y<\/em>-values of the lines.<\/p>\n

38. [latex]x+3<3x - 4[\/latex]\n\n39. [latex]x - 2>2x+1[\/latex]<\/p>\n

40. [latex]x+1>x+4[\/latex]<\/p>\n

41. [latex]\\frac{1}{2}x+1>\\frac{1}{2}x - 5[\/latex]<\/p>\n

42. [latex]4x+1<\\frac{1}{2}x+3[\/latex]\n\nFor the following exercises, write the set in interval notation.\n\n43. [latex]\\{x|-1<\/p>\n

52.
\n\"Number<\/p>\n

53.
\n\"Number<\/p>\n

For the following exercises, input the left-hand side of the inequality as a Y1 graph in your graphing utility. Enter y2 = the right-hand side. Entering the absolute value of an expression is found in the MATH menu, Num, 1:abs(. Find the points of intersection, recall (2nd<\/sup> CALC 5:intersection, 1st<\/sup> curve, enter, 2nd<\/sup> curve, enter, guess, enter). Copy a sketch of the graph and shade the x<\/em>-axis for your solution set to the inequality. Write final answers in interval notation.<\/p>\n

54. [latex]|x+2|-5< 2[\/latex]\n\n55. [latex]\\frac{-1}{2}|x+2|< 4[\/latex]\n\n56. [latex]|4x+1|-3> 2[\/latex]<\/p>\n

57. [latex]|x - 4|< 3[\/latex]\n\n58. [latex]|x+2|\\ge 5[\/latex]\n\n59.\u00a0Solve [latex]|3x+1|=|2x+3|[\/latex]\n\n60.\u00a0Solve [latex]{x}^{2}-x>12[\/latex]<\/p>\n

61. [latex]\\frac{x - 5}{x+7}\\le 0[\/latex], [latex]x\\ne -7[\/latex]<\/p>\n

62.\u00a0[latex]p=-{x}^{2}+130x - 3000[\/latex] is a profit formula for a small business. Find the set of x<\/em>-values that will keep this profit positive.<\/p>\n

63.\u00a0In chemistry the volume for a certain gas is given by [latex]V=20T[\/latex], where V<\/em> is measured in cc and T<\/em> is temperature in \u00baC. If the temperature varies between 80\u00baC and 120\u00baC, find the set of volume values.<\/p>\n

64.\u00a0A basic cellular package costs $20\/mo. for 60 min of calling, with an additional charge of $.30\/min beyond that time. The cost formula would be [latex]C=\\$20+.30\\left(x - 60\\right)[\/latex]. If you have to keep your bill lower than $50, what is the maximum calling minutes you can use?<\/p>\n

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CC licensed content, Specific attribution<\/div>