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. \[x+3<3 x-4\nonumber\]