Solve the inequality and graph the solution.

Question

r+1≥10
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 \( r + 1 \geq 10 \), we first isolate \( r \):

1. Subtract \( 1 \) from both sides: \[ r \geq 10 - 1 \] \[ r \geq 9 \]

The solution to the inequality is \( r \geq 9 \), which means that \( r \) can take any value greater than or equal to \( 9 \).

Graphing the Solution

1. End Points: The endpoint is \( 9 \). We'll represent this on the graph.

2. Closed/Open Endpoint: Since the inequality is \( \geq \) (greater than or equal to), we will represent \( 9 \) with a closed dot. If we were to change it to an open endpoint, we could choose to represent \( 9 \) with an open circle, but because the inequality specifically includes \( 9 \), it should remain closed.

3. Ray Representation: The solution will be a ray starting from \( 9 \) and extending to the right (towards positive infinity).

Final Graph:

• Plot a closed dot at \( 9 \) and shade the region to the right of \( 9 \) to represent all values of \( r \) that satisfy the inequality \( r \geq 9 \).

This can be visualized as follows:

<-----●=======================>
       9

• The dot at \( 9 \) is filled in indicating that \( 9 \) is part of the solution, and the shading indicates that all values greater than \( 9 \) are included in the solution.