Question

question
solve the following inequality algebraically.
|x + 8| ≤ 8

Explanation:

Step1: Recall absolute value inequality rule

For \(|A| \leq B\) (where \(B \geq 0\)), it is equivalent to \(-B \leq A \leq B\). Here, \(A = x + 8\) and \(B = 8\), so we get \(-8 \leq x + 8 \leq 8\).

Step2: Solve the left inequality

Subtract 8 from all parts: \(-8 - 8 \leq x + 8 - 8 \leq 8 - 8\).
Simplify: \(-16 \leq x \leq 0\).

Answer:

\(-16 \leq x \leq 0\)