Graphing Intervals on a Number Line

Graphing Intervals on a Number Line

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

Example 1

Graph the given interval on a number line. (1, 4)

[ ( , ) ] 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

Graph the given interval on a number line. [-2, 3]

' [ , ] ' 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

Graph the given interval on a number line. (-2, 1]

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

Graph the given interval on a number line. (6, infinity)

(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

Graph the given interval on a number line. (-infinity, 7)

(-∞, 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