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X X − 5 > 1 2 - Mathematics

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Question

$\frac{x}{x - 5} > \frac{1}{2}$

Solution

$\frac{x}{x - 5} > \frac{1}{2}$
$\Rightarrow \frac{x}{x - 5} - \frac{1}{2} > 0$
$\Rightarrow \frac{2 x - x + 5}{2 (x - 5)} > 0$
$\Rightarrow \frac{x + 5}{2 (x - 5)} > 0$
$\Rightarrow \frac{x + 5}{x - 5} > 0$

$∴ x \in (- \infty, - 5) \cup (5, \infty)$

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Inequalities - Introduction

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Chapter 15: Linear Inequations - Exercise 15.1 [Page 10]

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RD Sharma Mathematics [English] Class 11

Chapter 15 Linear Inequations
Exercise 15.1 | Q 28 | Page 10

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