Question:
Solve $\left|\frac{3 x-4}{2}\right| \leq \frac{5}{12}$
Solution:
As, $\left|\frac{3 x-4}{2}\right| \leq \frac{5}{12}$
$\Rightarrow-\frac{5}{12} \leq \frac{3 x-4}{2} \leq \frac{5}{12} \quad($ As,$|x| \leq a \Rightarrow-a \leq x \leq a)$
$\Rightarrow-\frac{5}{6} \leq 3 x-4 \leq \frac{5}{6}$
$\Rightarrow-\frac{5}{6}+4 \leq 3 x \leq \frac{5}{6}+4$
$\Rightarrow \frac{-5+24}{6} \leq 3 x \leq \frac{5+24}{6}$
$\Rightarrow \frac{19}{6} \leq 3 x \leq \frac{29}{6}$
$\Rightarrow \frac{19}{18} \leq x \leq \frac{29}{18}$
$\therefore x \in\left[\frac{19}{18}, \frac{29}{18}\right]$
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