Question

Solve $\left|3-4x\right|\ge 9$ [NCERT EXEMPLAR]

Answer 1

$$\begin{gathered} \mathrm{As},\left|3-4x\right|\ge 9 \\ \Rightarrow \left(3-4x\right)\le -9\mathrm{or}\left(3-4x\right)\ge 9\left(\mathrm{As},\left|x\right|\ge a\Rightarrow x\le -a\mathrm{or}x\ge a\right) \\ \Rightarrow -4x\le -9-3\mathrm{or}-4x\ge 9-3 \\ \Rightarrow -4x\le -12\mathrm{or}-4x\ge 6 \\ \Rightarrow x\ge \frac{-12}{-4}\mathrm{or}x\le \frac{6}{-4} \\ \Rightarrow x\ge 3\mathrm{or}x\le \frac{-3}{2} \\ \therefore x\in (-\infty ,\frac{-3}{2}]\cup [3,\infty ) \end{gathered}$$