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Mathematics LibreTexts

2.7.0: Linear Inequalities and Absolute Value Inequalities (Exercises)

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For the following exercises, solve the inequality. Write your final answer in interval notation.

60. 5x8<12
61. 2x+5>x7
62. x13+x+2535
63. |3x+2|+19
64. |5x1|>14
65. |x3|<4

For the following exercises, solve the compound inequality. Write your answer in interval notation.

66. 4<3x+218
67. 3y<12y<5+y

For the following exercises, graph as described.

68. Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation. |x+3|5


69. 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 -values of the lines. See the interval where the inequality is true. x+3<3x4


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