# How do you solve 2x-3<x+4<3x-2?

May 9, 2018

Isolate for x on both sides

#### Explanation:

I like to tackle them separately, so I get:

1. $2 x - 3 < x + 4$
2. $x + 4 < 3 x - 2$

Lets try to solve them by isolating for "x". but keep in mind we want our "x" term in the middle at the end so we will isolate "x" to the right side for 1 and to the left for 2

1.
$- 3 - 4 < x - 2 x$
$- 7 < - x$
$7 > x$ note: Sign switched because we divide by a negative number.

2.
$x + 4 < 3 x - 2$
$x - 3 x < - 2 - 4$
$- 2 x < - 6$
$x > 3$ note: Sign switched because we divide by a negative number.

So our final is...

$7 > x > 3$
or
$3 < x < 7$