Question

solve the following inequality. then graph the solution set.
|x| ≤ 9
b. the solution set is one or two points. the solution set is { }.
(type an integer or a fraction. use a comma to separate answers as needed.)
c. the solution set is ∅.
choose the correct graph below.
a.
b.
c.
d.
e.
f.

Explanation:

Step1: Rewrite absolute value inequality

Recall that $|x| \leq a$ translates to $-a \leq x \leq a$. For $a=8$, this gives:
$$-8 \leq x \leq 8$$

Step2: Identify solution set form

The solution is all real numbers between -8 and 8, inclusive. So the solution set is $\{-8, 8\}$ as the boundary points, representing the interval $[-8, 8]$.

Step3: Match to correct graph

A closed interval $[-8, 8]$ on a number line has filled circles at -8 and 8, with a line connecting them. This matches option C.

Answer:

The solution set is $\{-8, 8\}$ (representing $-8 \leq x \leq 8$)
Correct graph: Option C