Question

solve each inequality. graph the solution set and write it in interval notation.
|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
(simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in the expression.)

b. the solution 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 ∅.

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| > a\) (where \(a>0\)), the solution is \(x < -a\) or \(x > a\). Here, \(a = 8\), so we have \(x < - 8\) or \(x > 8\).

Step2: Write in interval notation

The interval for \(x < - 8\) is \((-\infty, - 8)\) and for \(x > 8\) is \((8, \infty)\). Combining these, the solution in interval notation is \((-\infty, - 8)\cup(8, \infty)\). Also, since it's an interval (not single points or empty set), we choose option A.

Answer:

A. The solution is an interval. The solution is \((-\infty, -8)\cup(8, \infty)\)