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 :)