# Inequalities - Representation on the Number Line

The numbers, which satisfy an inequality can be illustrated on a number line. For instance we may need to illustrate all the number that satisfy the inequality: $x < 5$ in other words we have to show all the numbers that make the inequality true.

To illustrate these numbers we'll often use a number line. For the inequality $$x < 5$$ this is shown here:

The following tutorial will teach us all we need to know about inequalities and number lines for now.

## Summary - Inequalities & Number Line

Following the tutorial we've just seen, below we list how to illustrate the four types of inequalities on the number line.

### Greater Than: $$x > a$$

$$x > a$$ is represented by an arrow with an empty dot above the $$a$$.
The arrow points in the direction of all the numbers that are greater than $$a$$.
The empty dot highlights that fact that $$x$$ cannot equal $$a$$:

### Greater Than Or Equal To: $$x \geq a$$

$$x \geq a$$ is represented by an arrow with an filled-in dot above the $$a$$.
The arrow points in the direction of all the numbers that are greater than $$a$$.
The filled-in dot highlights that fact that $$x$$ can be equal to $$a$$:

### Less Than: $$x < a$$

$$x < a$$ is represented by an arrow with an empty dot above the $$a$$.
The arrow points in the direction of all the numbers that are less than $$a$$.
The empty dot highlights that fact that $$x$$ cannot equal $$a$$:

### Less Than Or Equal To: $$x \leq a$$

$$x \leq a$$ is represented by an arrow with an filled-in dot above the $$a$$.
The arrow points in the direction of all the numbers that are less than $$a$$.
The filled-in dot highlights that fact that $$x$$ can be equal to $$a$$:

## Exercise

Illustrate the solutions to each of the following inequalities using the number line:

1. $$x \leq 4$$
2. $$x > -3$$
3. $$x < 6$$
4. $$x \geq 1$$
5. $$x \leq -1$$
6. $$x > 2$$

1. The solutions to $$x \leq 4$$ are all numbers less than or equal to $$4$$:

2. The solutions to $$x > -3$$ are all numbers greater than $$-3$$:

3. The solutions to $$x < 6$$ are all numbers less than $$6$$:

4. The solutions to $$x \geq 1$$ are all numbers greater than or equal to $$1$$:

5. The solutions to $$x \leq -1$$ are all numbers less than or equal to $$-1$$:

6. The solutions to $$x > 2$$ are all numbers greater than $$2$$: