Question

1. |10 + 4x| < 14

Explanation:

Step1: Rewrite absolute - value inequality

If \(|a| 0\)), then \(-b < a < b\). So for \(|10 + 4x|<14\), we have \(-14<10 + 4x<14\).

Step2: Subtract 10 from all parts

\(-14-10<10 + 4x-10<14 - 10\), which simplifies to \(-24<4x<4\).

Step3: Divide all parts by 4

\(\frac{-24}{4}<\frac{4x}{4}<\frac{4}{4}\), resulting in \(-6 < x < 1\).

Answer:

\(-6 < x < 1\)