Inequalities

Symbols

Inequalities involve expressions and/ or numbers that are not equal. They commonly use the symbols below to show that one is greater or lesser than another.

means Greater Than
< means Less Than
≥ means Greater Than Or Equal To
≤ means Less Than Or Equal To

Larger Side Greater, Smaller Side Lesser

A helpful way to remember what each symbol means is to look at the size of each side. As shown below, the value that is on the larger side is greater and the value on the smaller side is less.

Inequalities on a number line

Inequalities can be represented on a number line as shown in the inequalities below:

Note: the open circle above a number means it is not included as part of the solution to the inequality while the solid circle means that it is.
The examples below how inequalities can represent a range of solutions with an upper and lower limit.

 x greater than or equal to 4 and less than 9 shown on a numberline

Inequalities Worksheets

The worksheet below allows for practice with showing inequalities on number lines.

More Inequalities

The same inequality logic can be used with more complex expressions. The examples below show this

The sum of 4 and a number times 5 is greater than 244 + 5x > 24
A number multiplied by 6 minus 3 is less than 96x – 3 < 9
20 minus 5 times a number is less than or equal to 1020 – 5x ≤ 10
6 times a number plus 8 is greater than or equal to 326x + 8 ≥ 32

Solving Real-world Problems with Inequalities

Example problem

Sam needs at least $500 for his holiday. He has already saved $150. He has 7 months until his holiday. What is the minimum he must save each month?

We will use “x” to represent the unknown minimum that Sam
must save each month.
The amount he already has saved plus what he must save in
each of the 7 months must be greater than or equal to 500.
150 + 7x ≥ 500
Subtract 150 from both sides of the inequality150 – 150 + 7x ≥ 500 – 150
Divide both sides by 77x ÷ 7 ≥ 350 ÷ 7
Each month Sam must save $50 or morex ≥ 50

Try the problems on this inequalities and word problems worksheet for practice.