Question

use the drawing tool(s) to form the correct answer on th
what is the solution set of this compound inequality?
1 ≤ |x + 3| ≤ 4

Explanation:

Step1: Split compound inequality

Split into two inequalities:
$|x+3| \geq 1$ and $|x+3| \leq 4$

Step2: Solve $|x+3| \geq 1$

Apply absolute value rule:
$x+3 \leq -1$ or $x+3 \geq 1$
$x \leq -4$ or $x \geq -2$

Step3: Solve $|x+3| \leq 4$

Apply absolute value rule:
$-4 \leq x+3 \leq 4$
Subtract 3 from all parts:
$-7 \leq x \leq 1$

Step4: Find intersection of solutions

Combine the two solution sets:

1. Intersection of $x \leq -4$ and $-7 \leq x \leq 1$: $-7 \leq x \leq -4$
2. Intersection of $x \geq -2$ and $-7 \leq x \leq 1$: $-2 \leq x \leq 1$

Answer:

The solution set is $[-7, -4] \cup [-2, 1]$
(To graph this: plot closed points at -7, -4, -2, 1; draw line segments from -7 to -4, and from -2 to 1)