Inequality Number Lines. How to show inequalities on a number line such as x is more than 4.


Sometimes you will be asked in your math exams to show an inequality on a number line. To represent an inequality on a number line you will need to remember these four rules. Note that a is any number along the number line (x axis):

Rule 1 x > a (x is more than a)

Draw an unshaded circle at point a and draw an arrow going right.

Rule 2 x< a (x is less than a)

Draw an unshaded circle at point a and draw an arrow going left.

Rule 3 x ≥ a (x is more than or equal to a)

Draw a shaded circle at point a and draw an arrow going right.

Rule 4 x ≤ a (x is less than or equal to a)

Draw a shaded circle at point a and draw an arrow going left.

Notice that if the inequality is just less than or more than the circle is unshaded, and if the circle is less than or equal to or more than equal to then the circle is shaded.


Example 1

Represent x ≤ 4 on a number line.

Since the inequality is less than or equal to 4 you need to do a shaded circle at 4 and an arrow pointing to the left.

Example 2

Represent x > -2 on a number line.

This time the inequality is x is more than minus 2. So you need to draw an unshaded circle at -2 and an arrow pointing to the right.

Example 3

Represent x < -3 on a number line.

This time the inequality is x is less than minus 3. So you need to draw an unshaed circle at -3 and an arrow pointing to the left.

Example 4

Represent x ≥ -9 in a number line.

This time the inequality is x is more than or equal to minus 9. So you need to draw a shaded circle at -9 and an arrow point to the right.

Example 5

Solve the inequality 3x + 1 > -5

First solve this inequality in the same way as you would solve an equation.

3x > -6 (subtract 1 from both sides)

x > -2 (divide both sides of the equation by 3)

All you need to do know is show this inequality on a number line. You need to draw an unshaded circle and an arrow pointing to the right.

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