Number of integral values of $x$ satisfying the given inequality $| 3 x - 2 | \leq \frac{1}{2}$ are?
0

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Solution

The correct option is A 0
Given: $| 3 x - 2 | \leq \frac{1}{2}$
$\Rightarrow - \frac{1}{2} \leq 3 x - 2 \leq \frac{1}{2}$
$\Rightarrow - \frac{1}{2} + 2 \leq 3 x \leq \frac{1}{2} + 2$
$\Rightarrow \frac{3}{2} \leq 3 x \leq \frac{5}{2}$
$\Rightarrow \frac{1}{2} \leq x \leq \frac{5}{6}$
$\Rightarrow x \in [\frac{1}{2}, \frac{5}{6}]$
$∴$ the number of integral values of $x$ are $0.$

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