Question

Solve the inequality and represent the solution graphically on number line.
$2(x-1)<x+5,3(x+2)>2-x$

Answer 1

Red line is $y=2x-2$
Green line is $y=x+5$
black line $y=2-x$
blue line is $y=3x+6$
Since $2x-1<x+5for$ all $x<7$
and $3(x+2)>2-xforallx>-1$
So intersection of these $x\in (-1,7)$