Question

solve the absolute value inequality: |x + 12|+5 < 27. isolate the absolute value by subtracting 5 from both sides.

Explanation:

Step1: Isolate the absolute - value

Subtract 5 from both sides of the inequality \(|x + 12|+5<27\).
\(|x + 12|+5-5<27 - 5\)
\(|x + 12|<22\)

Step2: Rewrite the absolute - value inequality

If \(|a|0\)), then \(-b < a < b\). Here \(a=x + 12\) and \(b = 22\), so \(-22

Step3: Solve for \(x\)

Subtract 12 from all parts of the compound inequality.
\(-22-12\(-34

Answer:

\(-34