N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
c–4<5
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality $c-4<5$, we will first isolate $c$.

1. Add 4 to both sides: $$c-4+4<5+4$$ $$c<9$$

The solution to the inequality is $c<9$.

Graphing the Solution

1. Plot the endpoint: Since the inequality is strictly less than (indicated by the < symbol), we will use an open circle at $9$ to show that $9$ is not included in the solution set.

2. Draw a ray: Extend a ray to the left from the open circle at $9$, indicating that all values less than $9$ are included in the solution.

Summary

• The solution to the inequality is $c<9$.
• On the graph, there will be an open circle at $9$ with a ray extending to the left.

If you were to visualize this, it would look like:

<----(9)================>

Where (9) indicates the open circle at $9$ and the arrow indicates all numbers to the left of $9$ are included in the solution.