Q94 / 150 · MHT CET 2020 (12 Oct Shift 1) · Mathematics
If $|3 x-2| \leq \frac{1}{2} \quad$ then $x \in$
- Correct answerA$\left[\frac{1}{2}, \frac{5}{6}\right]$
- B$\left(\frac{1}{2}, \frac{5}{6}\right]$
- C$\left[\frac{1}{2}, \frac{5}{6}\right)$
- D$\left(\frac{1}{2}, \frac{5}{6}\right)$
Solution
We have $|3 x-2| \leq \frac{1}{2}$
$\therefore \frac{-1}{2} \leq(3 x-2) \leq \frac{1}{2}$
$\therefore \frac{-1}{2} \leq 3 x-2 \quad$ and $\quad 3 x-2 \leq \frac{1}{2}$
$\therefore \quad \frac{3}{2} \leq 3 x \quad$ and $\quad 3 x \leq \frac{5}{2}$
$\quad \frac{1}{2} \leq x \quad$ and $\quad x \leq \frac{5}{6}$
$\therefore x \in\left[\frac{1}{2}, \frac{5}{6}\right]$
Hence, the correct answer is option: 'A'.