Question

following inequality algebraically.
|x - 3| ≤ 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, \(a = x - 3\) and \(b = 8\).

Step2: Apply the rule to the given inequality

Substitute \(a = x - 3\) and \(b = 8\) into the rule: \(-8 \leq x - 3 \leq 8\).

Step3: Solve the compound inequality

Add 3 to all parts of the compound inequality: \(-8 + 3 \leq x - 3 + 3 \leq 8 + 3\).
Simplify each part: \(-5 \leq x \leq 11\).

Answer:

\(-5 \leq x \leq 11\)