Question

-2 < 3x+4 < 31 find x

Answer 1

First rewrite into 2 inequalities,

$-2\lt3x+4$

$3x+4\lt31$

Solve each of the inequalities,

$-2\lt3x+4\implies3x\gt-6\implies x\gt-2$

$3x+4\lt31\implies 3x\lt27\implies x\lt9$

So our x is between -2 and 9 which can be written as,

$-2\lt x\lt9$

or as an interval,

$x\in(-2,9)$

Hope this helps :)