Question

use the drawing tool(s) to form the correct answer on what is the solution set of this compound inequality? $3 \leq |x - 1| < 8$

Explanation:

Step1: Split absolute value inequality

Split into two inequalities:
$3 \leq x-1 < 8$ or $-8 < x-1 \leq -3$

Step2: Solve first inequality chain

Add 1 to all parts:
$3+1 \leq x < 8+1$
$4 \leq x < 9$

Step3: Solve second inequality chain

Add 1 to all parts:
$-8+1 < x \leq -3+1$
$-7 < x \leq -2$

Answer:

The solution set is $-7 < x \leq -2$ or $4 \leq x < 9$, which on a number line would have:

• An open point at $-7$, a closed point at $-2$, with a line segment connecting them
• An open point at $9$, a closed point at $4$, with a line segment connecting them