Question

question
solve the following inequality algebraically.
|x - 8| ≤ 3

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 \(B = 3\). So we get \(-3 \leq x - 8 \leq 3\).

Step2: Solve the compound inequality

Add 8 to all parts of the inequality.
Left part: \(-3 + 8 \leq x - 8 + 8\) which simplifies to \(5 \leq x\).
Right part: \(x - 8 + 8 \leq 3 + 8\) which simplifies to \(x \leq 11\).

Answer:

\(5 \leq x \leq 11\)