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

# Solve Each of the Following System of Equations in R. X + 5 > 2(X + 1), 2 − X < 3 (X + 2) - Mathematics

Solve each of the following system of equations in R.

x + 5 > 2(x + 1), 2 − x < 3 (x + 2)

#### Solution

$\text{ We have }, 4x - 1 \leq 0$
$\Rightarrow 4x \leq 1$
$\Rightarrow x \leq \frac{1}{4} (\text{ Dividing both the sides by } 4)$
$\Rightarrow x \in ( - \infty , \frac{1}{4}] . . . (i)$
$\text{ Also }, 3 - 4x < 0$
$\Rightarrow 0 > 3 - 4x$
$\Rightarrow 4x > 3$
$\Rightarrow x > \frac{3}{4} \text{ Dividing both sides by 4 }$
$\Rightarrow x \in \left( \frac{3}{4}, \infty \right) . . . (ii)$
$\text{ Hence, the solution of the given set of inequalities is the intersection of } (i) \text{ and } (ii) .$
$But, \left( - \infty \frac{1}{4} \right) \cap \left( \frac{3}{4}, \infty \right) = \phi$
$\text{ Thus, the given set of inequations has no solution } .$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.2 | Q 12 | Page 15