Question

Solve the inequalities
$2(x-1)<x+5,3(x+2)>2-x$

Answer 1

$2(x-1)<x+5\Rightarrow 2x-2<x+5\Rightarrow 2x-x<5+2$

$\Rightarrow x<\mathrm{7...}\left(1\right)$

$3(x+2)>2-z\Rightarrow 3x+6>2-x\Rightarrow 3x+x>2-6$

$\Rightarrow 4x>-4$

$\Rightarrow x>-\mathrm{1....}\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$ it can be concluded that the solution set for the given system of inequalities is $(-1,7)$.