Question

Find the integer solutions that

satisfy the inequality, 2 < x + 5<7.
Give your answer as an inequality.
Use the < or > signs to represent your
inequality

Answer 1

Given:

The compound inequality is:

`2<x+5<7`

To find:

The integer solutions that satisfy the given inequality.

Solution:

We have,

`2<x+5<7`

Subtracting 5 from each side, we get

`2-5<x+5-5<7-5`

`-3<x<2`

All the real numbers between -3 and 2 are in the solution set but -3 and 2 are not included in the solution set.

The integers between -3 and 2 are -2, -1, 0, 1.

Therefore, the integer solution of the given inequality are -2, -1, 0, 1. The answer as an inequality is
`-3<x<2`.