Question

The solution set for: $|3x-2|\le \frac{1}{2}$ is

• A. $[\frac{1}{2},\frac{5}{6}]$
• B. $[\frac{2}{3},\frac{1}{2}]$
• C. $[\frac{5}{6},\frac{1}{2}]$
• D. $[\frac{1}{2},\frac{2}{3}]$

Answer 1

The correct option is A $[\frac{1}{2},\frac{5}{6}]$

$|3x-2|\le \frac{1}{2}$
$3x-2\le \frac{1}{2}$ or $3x-2\ge \frac{-1}{2}$
$x\le \frac{5}{6}$ or $x\ge \frac{1}{2}$
$\therefore \frac{1}{2}\le x\le \frac{5}{6}$