Question

which set of numbers is included in the solution set of the compound inequality?
15 16 17 18 19 20 21 22 23 24 25
{−7, 5, 18, 24, 32}
{−9, 7, 15, 22, 26}
{16, 17, 22, 23, 24}
{18, 19, 20, 21, 22}

Explanation:

Step1: Identify inequality from number line

The number line has a closed dot at 18 (includes 18) pointing left, and an open dot at 22 (excludes 22) pointing right. So the compound inequality is $x \leq 18$ or $x > 22$.

Step2: Check each set against inequality

• Set 1 $\{-7, 5, 18, 24, 32\}$: $-7 \leq18$, $5\leq18$, $18\leq18$, $24>22$, $32>22$ → all values satisfy the inequality.
• Set 2 $\{-9, 7, 15, 22, 26\}$: $22$ does not satisfy ($x>22$ excludes 22, $x\leq18$ excludes 22) → fails.
• Set 3 $\{16, 17, 22, 23, 24\}$: $22$ does not satisfy the inequality → fails.
• Set 4 $\{18, 19, 20, 21, 22\}$: $19,20,21$ are between 18 and 22, so they satisfy neither $x\leq18$ nor $x>22$; $22$ also fails → fails.

Answer:

$\{-7, 5, 18, 24, 32\}$