2.7.0: Linear Inequalities and Absolute Value Inequalities (Exercises)

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. $$x+3<3 x-4\nonumber$$