Question

Solve  

\[\left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}\] 

Answer 1

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