Question

solve the absolute value inequality
|x + 6| ≤ 4

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set in interval notation is
(simplify your answer.)

b. the solution set is ∅

Explanation:

Step1: Recall absolute value inequality rule

For \(|u| \leq c\) (where \(c \geq 0\)), it is equivalent to \(-c \leq u \leq c\). Here, \(u = x + 6\) and \(c = 4\). So we get \(-4 \leq x + 6 \leq 4\).

Step2: Solve the compound inequality

Subtract 6 from all parts of the inequality: \(-4 - 6 \leq x + 6 - 6 \leq 4 - 6\).
Simplify each part: \(-10 \leq x \leq -2\).
In interval notation, this is \([-10, -2]\).

Answer:

A. The solution set in interval notation is \([-10, -2]\)