# Solve each of the following system of equations in R. 13. 2 (x − 6) < 3x − 7, 11 − 2x < 6 − x

Question:

Solve each of the following system of equations in R.

13. 2 (x − 6) < 3x − 7, 11 − 2x < 6 − x

Solution:

$2(x-6)<3 x-7$

$\Rightarrow 2 x-12<3 x-7$

$\Rightarrow 3 x-7>2 x-12$

$\Rightarrow 3 x-2 x>-12+7$

$\Rightarrow x>-5$

$\Rightarrow x \in(-5, \infty) \quad \ldots$ (i)

Also, $11-2 x<6-x$

$\Rightarrow 6-x>11-2 x$

$\Rightarrow 2 x-x>11-6$

$\Rightarrow x>5$

$\Rightarrow x \in(5, \infty) \quad \ldots$ (ii)

Hence, the solution of the given inequation is the intersection of (i) and (ii).

$(-5, \infty) \cap(5, \infty)=(5, \infty)$

Hence, the solution of the given inequation is $(5, \infty)$.