Question

Solve $\left|\frac{3x-4}{2}\right|\le \frac{5}{12}$

Answer 1

$$\begin{gathered} \mathrm{As},\left|\frac{3x-4}{2}\right|\le \frac{5}{12} \\ \Rightarrow -\frac{5}{12}\le \frac{3x-4}{2}\le \frac{5}{12}\left(\mathrm{As},\left|x\right|\le a\Rightarrow -a\le x\le a\right) \\ \Rightarrow -\frac{5}{6}\le 3x-4\le \frac{5}{6} \\ \Rightarrow -\frac{5}{6}+4\le 3x\le \frac{5}{6}+4 \\ \Rightarrow \frac{-5+24}{6}\le 3x\le \frac{5+24}{6} \\ \Rightarrow \frac{19}{6}\le 3x\le \frac{29}{6} \\ \Rightarrow \frac{19}{18}\le x\le \frac{29}{18} \\ \therefore x\in \left[\frac{19}{18},\frac{29}{18}\right] \end{gathered}$$