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

1 Answer
Jul 27, 2015

3 < x < 7 (In interval notation: (3, 7))

Explanation:

In order for 2x-3 < x+4 < 3x-2 to be true, the compound inequality:

2x-3 < x+4 " " AND " " x+4 < 3x-2 must be true.

Solving each individually, we get:

2x-3 < x+4 Subtract x and add 3 on both sides to get:

x < 7

We also need:

x+4 < 3x-2 Subtract x and add 2 on both sides to get:

6 < 2x, so 3 < x

The solution will require both 3 < x and x < 7.

The numbers that satisfy both inequalities simultaneously are the numbers between 3 and 7 (exclusive).