# Solve Each of the Following System of Equations in R. 3x − 6 > 0, 2x − 5 > 0 - Mathematics

Solve each of the following system of equations in R.

3x − 6 > 0, 2x − 5 > 0

#### Solution

$3x - 6 > 0$
$\Rightarrow 3x > 6$
$\Rightarrow x > 2$
$\Rightarrow x \in \left( 2, \infty \right) . . . \left( i \right)$
$\text{ Also }, 2x - 5 > 0$
$\Rightarrow 2x > 5$
$\Rightarrow x > \frac{5}{2}$
$\Rightarrow x \in \left( \frac{5}{2}, \infty \right) . . . \left( ii \right)$
$\text{ Solution of the given set of inequalities is the intersection of } \left( i \right) \text{ and } \left( ii \right) .$
$\left( 2, \infty \right) \cap \left( \frac{5}{2}, \infty \right) = \left( \frac{5}{2}, \infty \right)$
$\text{ Thus, the solution of the given set of inequalities is } \left( \frac{5}{2}, \infty \right) .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.2 | Q 5 | Page 15