Back to: Algebra 1

**How to Graph Inequalities**

We can graph inequalities on a number line to get a better idea of how they are behaving. The following steps illustrate the point

- Find the number on the other side of the inequality sign from the variable (like the 6 in
*x*> 6). - Sketch a number line and draw an open circle around that number.
- Fill in the circle if the variable
also equal that number.*can* - Shade all numbers the variable can be.

Here is what *y* ≤ 2 looks like:

Here is what y < 2 looks like:

Notice the difference between the two graphs. In the first graph, the circle around the 2 is colored in. This is because *y* ** can** be 2 in the first, but

**the second.**

*not***Note**. Use an open circle when given **<** (less than) or **>** (greater than). Use a closed circle when given** ≤** (less than or equal to) or **≥** (greater than or equal to).

**Example**: −1 ≤ 3n + 4 – 8

3 ≤ 3n

1 ≤ n

Graph the solution on a number line.

**n ≥ 1**

**Example**: −9 > 3n + 2 + 4

-15 > 3n

-5 > n

Graph the solution on a number line.

**Example**: 5x − 4 > + 2x + 8

3x > 12

x > 4

Graph the solution on a number line.

**Example**: – 10 – 6p < −(2p − 7) + 3

– 10 – 6p < – 2p + 10

– 20 < 4p

– 5 < p

Graph the solution on a number line.

**Example**: 9 − 3(t − 4) > −3

9 – 3t + 12 ≥ – 3

21 – 3t ≥ -3

– 3t ≥ – 24

t ≤ 8 When dividing by a negative quantity reverse the sign of inequality.

Graph the solution on a number line.

**Practice Problems 4**