Question

solve |h - 2| < 14. {h| < h < }

Explanation:

Step1: Recall absolute inequality rule

For \(|x| < a\) (\(a>0\)), it is equivalent to \(-a < x < a\). So for \(|h - 2| < 14\), we get \(-14 < h - 2 < 14\).

Step2: Solve left inequality

Add 2 to all parts. For the left part: \(-14 + 2 < h - 2 + 2\), which simplifies to \(-12 < h\).

Step3: Solve right inequality

For the right part: \(h - 2 + 2 < 14 + 2\), which simplifies to \(h < 16\).

Answer:

\(-12 < h < 16\)