Question

solve the following inequality. then graph the solution set. |x| ≤ 8 select the correct choice below, and, if necessary, fill in the answer box to complete your choice. a. the solution is an interval. the solution is \\(\square\\) (simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in the expression) b. the solution set is one or two points. the solution set is \\(\square\\) (type an integer or a fraction. use a comma to separate answers as needed) c. the solution set is \\(\varnothing\\). choose the correct graph below. a. graph a b. graph b c. graph c d. graph d

Explanation:

Step1: Rewrite absolute value inequality

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

Step2: Write in interval notation

The interval for all real numbers between -8 and 8 (inclusive) is:
$$[-8, 8]$$

Step3: Match to correct graph

The graph for $[-8, 8]$ has closed dots at -8 and 8, with a solid line connecting them.

Answer:

A. The solution is an interval. The solution is $[-8, 8]$.
C. (The graph with closed dots at -8 and 8, solid line between them)