Section 2.5 Additional Practice Solving Absolute Value Equations and Inequalities
¶Exercises Exercises
Determine the solution set for each equation and inequality.
1.
|2x−4|=12
The solution set is \(\{-4,8\}\text{.}\)
2.
|3−x|=−4
The solution set is \(\emptyset\text{.}\)
3.
|5−7t|=11
The solution set is \(\left\{-\frac{6}{7},\frac{16}{7}\right\}\text{.}\)
4.
|y+7|=7
The solution set is \(\{-14,0\}\text{.}\)
5.
|32x−9|=9
The solution set is \(\{0,12\}\text{.}\)
6.
|w+53|=15
The solution set is \(\{-50,40\}\text{.}\)
7.
|2x+7|≤14
The solution set is \(\left[-\frac{21}{2},\frac{7}{2}\right]\text{.}\)
8.
|10−y|<22
The solution set is \((-12,32)\text{.}\)
9.
|22+17x|≤−11
The solution set is \(\emptyset\text{.}\)
10.
|43t+8|≤24
The solution set is \([-24,12]\text{.}\)
11.
|8−x5|≤14
The solution set is \([-62,78]\text{.}\)
12.
|z+12|≤0
The solution set is \(\{-12\}\text{.}\)
13.
|3x+7|≥−19
The solution set is \((-\infty,\infty)\text{.}\)
14.
|2x+31|≥17
The solution set is \((-\infty,-24] \cup [-7,\infty)\text{.}\)
15.
|−12w+7|>21
The solution set is \((-\infty,-28) \cup (56,\infty)\text{.}\)
16.
|−5x+7|≥27
The solution set is \((-\infty,-4] \cup \left[\frac{34}{5},\infty\right)\text{.}\)
17.
|4x+2|>0
The solution set is \(\left(-\infty,-\frac{1}{2}\right) \cup \left(-\frac{1}{2},\infty\right)\text{.}\)
18.
|7−2x3|>4
The solution set is \(\left(-\infty,-\frac{5}{2}\right) \cup \left(\frac{19}{2},\infty\right)\text{.}\)
19.
5−|2x+3|=−8
The solution set is \(\{-8,5\}\text{.}\)
20.
|y+73|−8≥−4
The solution set is \((-\infty,-19] \cup [5,\infty)\text{.}\)
21.
17−|1−x3|≥12
The solution set is \([-14,16]\text{.}\)
22.
18+3|−12t|<24
The solution set is \((-4,4)\text{.}\)
23.
12+|w−9|=10
The solution set is \(\emptyset\text{.}\)
24.
−|3+2x|+62>1
The solution set is \(\left(-\frac{7}{2},\frac{1}{2}\right)\text{.}\)