Inequalities are a branch of algebra that is very closely linked to equations. You will be very familiar by this point of how to solve equations and the good news is that you use exactly the same method to solve inequalities.

**What is an ****inequality****?**

Inequality just means 'not equal to' so instead of using the = symbol like we do in an equation we use one of the four following symbols.

< Less than

> Greater than

≥ Greater than or equal to

≤ Less than or equal to

**Solving an inequality;**

**Example 1: Solve x + 4 < 3**

We do this exactly the same way we would an equation.

x + 4 - 4 < 3 - 4

x < -1

What this means is that if you put any number that is less than -1 (-2, -3, -4, -2.1 etc) into the original equation, it would be true.

**Example 2: Solve x/2 > 7**

We do this exactly the same way we would an equation.

x/2 x 2 > 7 x 2

x > 14

**The special case**

There is one special case that we need to be aware of. If we had...

5 < x + 3

5 - 3 < x + 3 - 3

2 < x

The issue here is that the x is on the right. If this was an equation, we would just swap them around but we can't quite do that with an inequality.

The inequality currently means '2 is less than x' so if we want the x on the left, we would have to say 'x is greater than 2'.

So 2 < x is the same as x > 2

If you want to switch an inequility over, **remember you have to swap the sign. **