# Graphing Linear Inequalities on a Number Line

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

## Example 1

[ > ] 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

[ ≥ ] 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

[ < ] 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

[ ≤ ] 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, ... .