Question

give the solution set in both interval and graph form.
$|x| > 3$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is .
(type your answer in interval notation. simplify your answer. use integers or fractions for any numbers in the expression.)
b. the solution set is $\emptyset$.

Explanation:

Step1: Rewrite absolute value inequality

The absolute value inequality $|x| > 3$ splits into two cases:
$x > 3$ or $x < -3$

Step2: Write in interval notation

For $x < -3$, the interval is $(-\infty, -3)$. For $x > 3$, the interval is $(3, \infty)$. Combine them with a union:
$(-\infty, -3) \cup (3, \infty)$

Step3: Verify solution validity

The inequality has valid solutions, so it is not an empty set.

Answer:

A. The solution set is $(-\infty, -3) \cup (3, \infty)$.

Graph form note: On a number line, draw open circles at $x=-3$ and $x=3$, then shade all regions to the left of $-3$ and to the right of $3$.