# 8.1: 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. $$5 x-8<12$$
61. $$-2 x+5>x-7$$
62. $$\frac{x-1}{3}+\frac{x+2}{5} \leq \frac{3}{5}$$
63. $$|3 x+2|+1 \leq 9$$
64. $$|5 x-1|>14$$
65. $$|x-3|<-4$$

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

66. $$-4<3 x+2 \leq 18$$
67. $$3 y<1-2 y<5+y$$

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. $|x+3| \geq 5\nonumber$
69. Graph both straight lines (left-hand side being $$y^{-1}$$ 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. $x+3<3 x-4\nonumber$

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