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 $-3<x<2$.