Finding the solution set for inequalities is quite straight forward as long as you treat them exactly the same as equation.

**1) Get rid of things by doing the opposite.**

**2) Do the same to both sides**

The main thing that is different (apart from the signs) is that we cannot just move the x to the other side.

In equations 1 = x and x = 1 are the same thing.

In inequalities, if we want to change the side x is on, we have to change the inequality as well.

so 1 < x would be the same as x > 1

**Example 1: Find the solution set for 3x + 5 ≤ 2**

We are trying to get X by itself, so we first need to get rid of the +5, we do this by subtracting 5.

3x + 5 - 5 ≤ 2 - 5

3x ≤ -3

Next, we have to eliminate the multiply by 3, we do this by dividing by 3

3x ÷ 3 ≤ -3 ÷ 3

x ≤ -1

**Example 1: Find the solution set for -2 > 3x + 4**

We are trying to get X by itself, so we first need to get rid of the +5, we do this by subtracting 5.

-2 - 4 > 3x + 4 - 4

-6 > 3x

Next, we have to eliminate the multiply by 3, we do this by dividing by 3

- 6 ÷ 3 > 3x ÷ 3

-2 > x

Lastly, this has the x on the right and it needs to be on the left. To do this, we also have to switch the inequality.

x < -2