Question

solve the following inequality. then graph the solution set.\\(|x|\leq 4\\\\\text{select the correct choices below, and, if necessary, fill in the answer box to complete your choice.}\
\bigcirc\text{ a. the solution is an interval. the solution is }\square.\
\quad\quad\text{(simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in}\
\quad\quad\text{the expression.)}\
\bigcirc\text{ b. the solution set is one or two points. the solution set is }\\{\square\\}.\
\quad\quad\text{(type an integer or a fraction. use a comma to separate answers as needed.)}\
\bigcirc\text{ c. the solution set is }\varnothing.

Explanation:

Step1: Recall absolute value inequality rule

The absolute value inequality \(|x| \leq a\) (where \(a \geq 0\)) is equivalent to \(-a \leq x \leq a\). For \(|x| \leq 4\), we apply this rule.

Step2: Solve the compound inequality

From the rule, we get \(-4 \leq x \leq 4\). In interval notation, this is written as \([-4, 4]\). Also, since the solution is a range of values (an interval) rather than just one or two points, option A is the correct choice.

Answer:

A. The solution is an interval. The solution is \([-4, 4]\)