Question

Solve  \[\left| 3 - 4x \right| \geq 9\]

Answer 1

\[\text{ As }, \left| 3 - 4x \right| \geq 9\]
\[ \Rightarrow \left( 3 - 4x \right) \leq - 9 \text{ or } \left( 3 - 4x \right) \geq 9 \left( As, \left| x \right| \geq a \Rightarrow x \leq - a \text{ or } x \geq a \right)\]
\[ \Rightarrow - 4x \leq - 9 - 3 \text{ or } - 4x \geq 9 - 3\]
\[ \Rightarrow - 4x \leq - 12 \text{ or } - 4x \geq 6\]
\[ \Rightarrow x \geq \frac{- 12}{- 4} \text{ or } x \leq \frac{6}{- 4}\]
\[ \Rightarrow x \geq 3 \text{ or } x \leq \frac{- 3}{2}\]
\[ \therefore x \in ( - \infty , \frac{- 3}{2}] \cup [3, \infty )\]