Solve the inequality and graph the solution.

Question

r–4<1
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( r - 4 < 1 \), we first isolate \( r \) on one side:

1. Add \( 4 \) to both sides: \[ r < 1 + 4 \] \[ r < 5 \]

Now, the solution to the inequality is:

\[ r < 5 \]

Graphing the Solution

1. Endpoints: The endpoint of the inequality is \( 5 \).
2. Type of endpoint: Since this is a strict inequality (\(<\)), we use an open circle at \( 5 \) to indicate that \( 5 \) is not included in the solution.
3. Direction of the solution: The solution extends to negative infinity (to the left of \( 5 \)).

Final Graph Representation

• Draw a number line.
• Place an open circle at \( 5 \).
• Shade the line to the left of \( 5 \) to indicate all numbers less than \( 5 \).

Summary

The solution to the inequality \( r - 4 < 1 \) is \( r < 5 \), represented graphically with an open circle at \( 5 \) and shading to the left of it.