Absolute Value Inequalities (with Interval Notation) Coloring Activity - Free Printable

Here is the solution to the absolute value inequalities:

1. $|x + 4| < 2$
- This inequality means that the distance between $x$ and $-4$ is less than 2.
- We can split this into two inequalities:
- $x + 4 < 2 \Rightarrow x < -2$
- $x + 4 > -2 \Rightarrow x > -6$
- Combining these gives the solution: $-6 < x < -2$

2. $|3m| \ge 9$
- This inequality means that the distance of $3m$ from 0 is greater than or equal to 9.
- We can split this into two inequalities:
- $3m \ge 9 \Rightarrow m \ge 3$
- $3m \le -9 \Rightarrow m \le -3$
- Combining these gives the solution: $m \le -3$ or $m \ge 3$

3. $|2p - 7| > 3$
- This inequality means that the distance of $2p - 7$ from 0 is greater than 3.
- We can split this into two inequalities:
- $2p - 7 > 3 \Rightarrow 2p > 10 \Rightarrow p > 5$
- $2p - 7 < -3 \Rightarrow 2p < 4 \Rightarrow p < 2$
- Combining these gives the solution: $p < 2$ or $p > 5$

4. $|6k + 3| \le 15$
- This inequality means that the distance of $6k + 3$ from 0 is less than or equal to 15.
- We can split this into two inequalities:
- $6k + 3 \le 15 \Rightarrow 6k \le 12 \Rightarrow k \le 2$
- $6k + 3 \ge -15 \Rightarrow 6k \ge -18 \Rightarrow k \ge -3$
- Combining these gives the solution: $-3 \le k \le 2$