Graphing Linear Inequalities on a Number Line

Graphing Linear Inequalities on a Number Line

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

Example 1

Graph the given inequality on a number line. x > 2

[ > ] means [greather than].

So x > 2 means
x is greater than 2.

[ > ] doesn't include [ = ]: equal to.

So draw an empty circle on x = 2.
(which means
x = 2 is not included in the inequality.)

And draw an arrow
that includes x = 3, 4, 5, ... (not 2).

Example 2

Graph the given inequality on a number line. y >= -1

[ ≥ ] means [greather than or equal to].

So y ≥ -1 means
y is greater than or equal to -1.

[ ≥ ] includes [ = ]: equal to.

So draw a full circle on y = -1.
(which means
y = -1 is included in the inequality.)

And draw an arrow
that includes y = -1, 0, 1, ... .

Example 3

Graph the given inequality on a number line. k < 8

[ < ] means [lesser than].

So k < 8 means
k is lesser than 8.

[ < ] doesn't include [ = ].

So draw an empty circle on k = 8.
(which means
k = 8 is not included in the inequality.)

And draw an arrow
that includes k = 7, 6, 5, ... (not 8).

Example 4

Graph the given inequality on a number line. p <= 1.5

[ ≤ ] means [lesser than or equal to].

So p ≤ 1.5 means
p is lesser than or equal to 1.5.

[ ≤ ] does include [ = ].

So draw a full circle on p = 1.5.
(which means
p = 1.5 is included in the inequality.)

So draw a full circle on p = 1.5.

And draw an arrow
that includes p = 1.5, 1, 0, -1, ... .