Inequalities

In a Nutshell

Inequalities say one side is bigger (or smaller) than the other — think of the symbol as a hungry crocodile eating the larger number.

An inequality compares two values using one of four symbols:

$<$ means "is less than"
$>$ means "is greater than"
$\leq$ means "is less than or equal to"
$\geq$ means "is greater than or equal to"

Unlike an equation (which has one answer), an inequality usually has many solutions. For example, $x > 3$ is satisfied by 4, 5, 3.1, 100 — any number greater than 3.

We show inequalities on a number line. An open circle means the value is not included (strict inequality), and a filled circle means it is included.

Variable Operator Value

Change the operator and value to see how the number line updates. Notice the difference between open and filled circles.

Watch it work

Question: Solve $x + 4 > 9$ and show the solution on a number line.

Have a go

Q1. List the integers that satisfy $-2 < x \leq 3$ .

Q2. Solve $x - 3 \geq 7$ .

Q3. Solve $2x < 14$ .

Q4. Write the inequality shown by an open circle at 4 with shading to the left.