Question

Solve the inequality and represent the solution graphically on number line.
$5(2x-7)-3(2x+3)\le 0,2x+19\le 6x+47$

Answer 1

We have,
$5(2x-7)-3(2x+3)\le 0$
$\Rightarrow 10x-35-6x-9\le 0$
$\Rightarrow 4x-44\le 0\Rightarrow x\le 11$
And $2x+19\le 6x+47$
$\Rightarrow 2x-6x\le 47-19$
$\Rightarrow -4x\le 28\Rightarrow x\ge -7$
Thus using above two we have $-7\le x\le 11$
Solution is also shown graphically