Absolute Value Inequalities Worksheet with Answer Key

What's on the worksheet

1. Solve each absolute value inequality and write the answer in interval notation.
   |x - 7| < 4|3x + 6| \le 12|x + 2| \ge 6\left|\dfrac{x}{2} - 1\right| < 3|6 - 5x| > 4
2. Isolate the absolute value first, then solve, or write no solution.
   4 - \dfrac{1}{2}|x + 2| > 3\dfrac{|2x - 1|}{3} + 4 \ge 7-2|x - 5| \ge -104|x + 3| + 7 < 7-3|x - 2| \le 6
3. List every integer that satisfies each absolute value condition.
4. Write an absolute value inequality whose solution is each given set.
5. Check Malik's steps for an absolute value inequality and find the error.
6. Solve an inequality with a number k, then find the value of k that fits a condition.
7. Hiro's hike: write and solve the distance condition for where he can camp.