Graphing Inequalities on a Number Line Examples

Graph the following inequality:

3 < x or x ≤ 4

x can be anything greater than 3 or less than or equal to 4. This includes all numbers on the number line, so we need to shade the entire thing!

Graph the following inequality:

-5 ≤ p < 5

p can be anything greater than or equal to -5 and less than 5. This means that it can only be the stuff in between.

Graph the following inequality:

y < -2 and y > 1

If this were an "or" inequality it would look like this:

However, we're dealing with an "and" inequality, so we only graph the numbers that overlap. Hmm…there don't seem to be any numbers that overlap. This means that no numbers satisfy both conditions. Our answer should look like this:

No solution!