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 can also equal that number.
- 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 not the second.
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