Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 2 X + 3 4 − 3 < X − 4 3 − 2 - Mathematics

$\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2$

#### Solution

$\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2$
$\Rightarrow \frac{2x + 3}{4} - \frac{x - 4}{3} < - 2 + 3 (\text{ Transposing } \frac{x - 4}{3} \text{ to the LHS }\hspace{0.167em} \text{ and - 3 to the RHS })$
$\Rightarrow \frac{3\left( 2x + 3 \right) - 4\left( x - 4 \right)}{12} < 1$
$\Rightarrow 3\left( 2x + 3 \right) - 4\left( x - 4 \right) < 12 (\text{ Multiplying both the sides by } 12)$
$\Rightarrow 6x + 9 - 4x + 16 < 12$
$\Rightarrow 2x + 25 < 12$
$\Rightarrow 2x < 12 - 25$
$\Rightarrow 2x < - 13$
$\Rightarrow x < - \frac{13}{2} (\text{ Dividing both the sides by 2 })$
$\text{ Hence, the solution of the given inequation is } \left( - \infty , - \frac{13}{2} \right) .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.1 | Q 14 | Page 10