Question

question
solve the following inequality algebraically.
|x + 5| ≤ 11

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, \(a = x + 5\) and \(b = 11\) (and \(11\geq0\)). So we can rewrite the inequality \(|x + 5| \leq 11\) as \(-11 \leq x + 5 \leq 11\).

Step2: Solve the compound inequality

Subtract 5 from all parts of the compound inequality.
For the left - hand side: \(-11-5\leq x + 5-5\), which simplifies to \(-16\leq x\).
For the right - hand side: \(x + 5-5\leq11 - 5\), which simplifies to \(x\leq6\).

Answer:

\(-16\leq x\leq6\)