solve 5 < x -2 < 11

Answer 1

To solve the compound inequality 5 < x - 2 < 11, we need to isolate the variable x.

First, we isolate x in the first inequality:
5 < x - 2

Adding 2 to both sides:
5 + 2 < x - 2 + 2
7 < x

Now, we isolate x in the second inequality:
x - 2 < 11

Adding 2 to both sides:
x - 2 + 2 < 11 + 2
x < 13

So, combining the two inequalities, we have:
7 < x < 13