Section 1.5 Additional Practice Solving Absolute Value Equations and Inequalities
¶Exercises Exercises
Determine the solution set for each equation and inequality.
1.
\(\abs{2x-4}=12\)
The solution set is \(\{-4,8\}\text{.}\)
2.
\(\abs{3-x}=-4\)
The solution set is \(\emptyset\text{.}\)
3.
\(\abs{5-7t}=11\)
The solution set is \(\left\{-\frac{6}{7},\frac{16}{7}\right\}\text{.}\)
4.
\(\abs{y+7}=7\)
The solution set is \(\{-14,0\}\text{.}\)
5.
\(\abs{\frac{3}{2}x-9}=9\)
The solution set is \(\{0,12\}\text{.}\)
6.
\(\abs{\frac{w+5}{3}}=15\)
The solution set is \(\{-50,40\}\text{.}\)
7.
\(\abs{2x+7} \le 14\)
The solution set is \(\left[-\frac{21}{2},\frac{7}{2}\right]\text{.}\)
8.
\(\abs{10-y} \lt 22\)
The solution set is \((-12,32)\text{.}\)
9.
\(\abs{22+17x} \le -11\)
The solution set is \(\emptyset\text{.}\)
10.
\(\abs{\frac{4}{3}t+8} \le 24\)
The solution set is \([-24,12]\text{.}\)
11.
\(\abs{\frac{8-x}{5}} \le 14\)
The solution set is \([-62,78]\text{.}\)
12.
\(\abs{z+12} \le 0\)
The solution set is \(\{-12\}\text{.}\)
13.
\(\abs{3x+7} \ge -19\)
The solution set is \((-\infty,\infty)\text{.}\)
14.
\(\abs{2x+31} \ge 17\)
The solution set is \((-\infty,-24] \cup [-7,\infty)\text{.}\)
15.
\(\abs{-\frac{1}{2}w+7} \gt 21\)
The solution set is \((-\infty,-28) \cup (56,\infty)\text{.}\)
16.
\(\abs{-5x+7} \ge 27\)
The solution set is \((-\infty,-4] \cup \left[\frac{34}{5},\infty\right)\text{.}\)
17.
\(\abs{4x+2} \gt 0\)
The solution set is \(\left(-\infty,-\frac{1}{2}\right) \cup \left(-\frac{1}{2},\infty\right)\text{.}\)
18.
\(\abs{\frac{7-2x}{3}} \gt 4\)
The solution set is \(\left(-\infty,-\frac{5}{2}\right) \cup \left(\frac{19}{2},\infty\right)\text{.}\)
19.
\(5-\abs{2x+3}=-8\)
The solution set is \(\{-8,5\}\text{.}\)
20.
\(\abs{\frac{y+7}{3}}-8 \ge -4\)
The solution set is \((-\infty,-19] \cup [5,\infty)\text{.}\)
21.
\(17-\abs{\frac{1-x}{3}} \ge 12\)
The solution set is \([-14,16]\text{.}\)
22.
\(18+3\abs{-\frac{1}{2}t} \lt 24\)
The solution set is \((-4,4)\text{.}\)
23.
\(12+\abs{w-9}=10\)
The solution set is \(\emptyset\text{.}\)
24.
\(\frac{-\abs{3+2x}+6}{2} \gt 1\)
The solution set is \(\left(-\frac{7}{2},\frac{1}{2}\right)\text{.}\)