# Graphing Intervals on a Number Line

How to graph intervals on a number line: examples and their solutions.

## Example 1

[ ( , ) ] is called an open interval.

It means the inequality signs don't include [ = ].

So the interval (1, 4) means 1 < *x* < 4:*x* is greater than 1 and lesser than 4.

To graph the interval:

Draw empty circles on 1 and 4.

(which means the interval doesn't include 1 and 4.)

And draw a line between the circles.

Graphing an interval is similar to

graphing a linear inequality on a number line.

## Example 2

' [ , ] ' is called a closed interval.

It means the inequality signs do include [ = ].

So the interval [-2, 3] means -2 ≤ *x* ≤ 3:*x* is greater than or equal to -2

and lesser than or equal to 3.

To graph the interval:

Draw full circles on -2 and 3.

(which means the interval includes -2 and 3.)

And draw a line between the circles.

## Example 3

Open and closed intervals can be mixed like this.

To graph the interval:

Draw an empty circle on -2 and a full circle on 1.

(which means the interval

doesn't include -2 and does include 1.)

And draw a line between the circles.

## Example 4

(6, ∞) means 6 < *x* < ∞.

∞ is the infinity.

(Technically, ∞ is not a number.

But let's just think it as the greatest number.)

So it's obvious that *x* < ∞.

So you can write 6 < *x* < ∞

as 6 < *x*,

which is *x* > 6.

Graph the inequality *x* > 6.

Graphing linear inequalities on a number line - Example 1

## Example 5

(-∞, 7] means -∞ < *x* ≤ 7.

-∞ is the negative infinity.

(Just like ∞, -∞ is also not a number.

But let's just think it as the least number.)

So it's obvious that -∞ < *x*.

So you can write -∞ < *x* ≤ 7

as *x* ≤ 7.

Graph the inequality *x* ≤ 7.

Graphing linear inequalities on a number line - Example 4