If $|3 x-2| \leq \frac{1}{2} \quad$ then $x \in$

If $|3 x-2| \leq \frac{1}{2} \quad$ then $x \in$
  1. $\left[\frac{1}{2}, \frac{5}{6}\right]$
  2. $\left(\frac{1}{2}, \frac{5}{6}\right]$
  3. $\left[\frac{1}{2}, \frac{5}{6}\right)$
  4. $\left(\frac{1}{2}, \frac{5}{6}\right)$

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 $\quad x \leq \frac{5}{6}$ $\therefore x \in\left[\frac{1}{2}, \frac{5}{6}\right]$

Asked in: MHT CET 2020 (12 Oct Shift 1)

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