# Solve ∣ ∣ ∣ 3 X − 4 2 ∣ ∣ ∣ ≤ 5 12 - Mathematics

Solve

$\left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}$

#### Solution

$\text{ As }, \left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}$
$\Rightarrow - \frac{5}{12} \leq \frac{3x - 4}{2} \leq \frac{5}{12} \left( \text{ As }, \left| x \right| \leq a \Rightarrow - a \leq x \leq a \right)$
$\Rightarrow - \frac{5}{6} \leq 3x - 4 \leq \frac{5}{6}$
$\Rightarrow - \frac{5}{6} + 4 \leq 3x \leq \frac{5}{6} + 4$
$\Rightarrow \frac{- 5 + 24}{6} \leq 3x \leq \frac{5 + 24}{6}$
$\Rightarrow \frac{19}{6} \leq 3x \leq \frac{29}{6}$
$\Rightarrow \frac{19}{18} \leq x \leq \frac{29}{18}$
$\therefore x \in \left[ \frac{19}{18}, \frac{29}{18} \right]$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.3 | Q 3 | Page 22