Solving inequalities is very simple if you follow a few simple rules.

1) Deal with them the same way as an equation.

2) If you want to switch the x in a solution set, you have to switch the sign (i.e. 1 > x is the same as x > 1)

A quick word on the language, when you are dealing with equations, you aren't finding a solution (this is for equations), you are finding a solution set.

**Example 1: Find the solutions for 2x + 1 < 5x + 3**

Step 1: We have a value of x on both sides, so we have to get rid of one of them, always get rid of the smaller one (this helps to avoid negatives)

3x + 1 < 5x + 3

3x + 1 - 3x < 5x + 3 - 3x

1 < 2x + 3

Step 2: Isolate the X

1 < 2x + 3

1 - 3 < 2x + 3 - 3

-2 < 2x

-2 ÷ 2< 2x ÷ 2

-1 < x

Step 3: Switch the inequality if necessary

x > -1

**Example 2: Find the solutions for -5 ≤ 3x + 1 ≤ 7**

We have three parts here, the key thing to remember is that we have to do the same to all the parts of the inequality

-5 ≤ 3x + 1 ≤ 7

-5 - 1 ≤ 3x + 1 - 1 ≤ 7 - 1

-6 ≤ 3x ≤ 6

-6 ÷ 3≤ 3x ÷ 3 ≤ 6 ÷ 3

-2 ≤ x ≤ 2