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.