Solve Inequalities

This activity is about solving inequalities.

 

Inequalities will give you a range of answers for an unknown which could be greater than (>), greater than or equal to (≥), less than (<), less than or equal to (≤).

 

They are solved in the same way as equations, either by working backwards doing inverses, or carrying out the same operation to each side.

 

For example:

4x - 6 > 26

Solve it exactly as if it were an equals sign.

 

Add 6 to both sides:

4x - 6 + 6 > 26 + 6

4x > 32

 

Divide both sides by 4:

x > 8

So, we know that x > 8

 

Just one operation needs care - multiplying or dividing each side by a negative number will reverse the inequality sign.

 

This can be illustrated as follows:

 

We know that 10 > 4

Multiplying each side by -2 gives -20 > -8 

 

This is obviously NOT TRUE

Reversing the sign makes it correct -20 < -8 

 

Let's have a go at some questions now.