When we are dealing with inequalities, one of the things we have to do is to state all the numbers that satisfy an inequality. We can either do this by giving a solution set or by drawing the numbers on a number line.

**Example 1: Illustrate the inequality 3x – 4 > 2 on a number line.**

The first step here is to solve the inequality.

3x – 4 + 4> 2 + 4

3x > 6

3x ÷ 3 > 6 ÷ 3

x > 2

Now we have the solution set, we can draw this on a number line.

As the inequality is **greater than,** we use an **unshaded circle** to show the value of 2. We know that the solutions are greater than 2, so we draw an arrow to the right.

**Example 2: Illustrate the inequality 2x + 1 ≤ 5 on a number line.**

The first step here is to solve the inequality.

2x + 1 ≤ 5

2x + 1 -1 ≤ 5 - 1

2x ≤ 4

2x ÷ 2 ≤ 4 ÷ 2

x ≤ 2

Now we have the solution set, we can draw this on a number line.

As the inequality is **less than or equal to**, we use a **shaded circle** to show the value of 2. We know that the solutions are less than or equal 2, so we draw an arrow to the left.

**Example 2: Illustrate the inequality -1 ≤ 2x – 3 < 5 on a number line.**

The first step here is to solve the inequality.

-1 + 3 ≤ 2x – 3 + 3 < 5 + 3

2 ≤ 2x < 8

2 ÷ 2 ≤ 2x ÷ 2 < 8 ÷ 2

1 ≤ x < 4

Now we have the solution set, we can draw this on a number line.

We can see that the solutions are between 1 and 4. The circle at 1 has to be shaded as it is ≤ and the one at 4 has to be unshaded.