Solve the inequality and graph the solution.

Question

85≤17(g–3)
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 \( 85 \leq 17(g - 3) \), we can start by isolating \( g \).

1. Distribute the 17 on the right side: \[ 85 \leq 17g - 51 \]

2. Add 51 to both sides: \[ 85 + 51 \leq 17g \] \[ 136 \leq 17g \]

3. Divide both sides by 17: \[ \frac{136}{17} \leq g \] \[ 8 \leq g \] or equivalently, \[ g \geq 8 \]

Graphing the Solution:

• The inequality \( g \geq 8 \) indicates that \( g \) can be any number greater than or equal to 8.
• In the graph:
  • Use a closed dot at 8 to indicate that 8 is included in the solution.
  • Shade to the right of 8 to indicate all values greater than 8 are also part of the solution.

Summary of the Steps:

• We found that \( g \geq 8 \).
• We will plot the point 8 (closed dot).
• We will shade all values to the right (to represent \( g \) values that are greater than 8).

If you want to change the endpoint from closed to open, you would have to change the inequality to strict (like \( g > 8 \)), causing the graph to have an open dot instead. In this specific case, since the original inequality was \( g \geq 8 \), we use a closed dot. However, if you were to do \( g > 8 \), it would be an open dot at 8.

Conclusion:

For the inequality \( g \geq 8 \):

• The solution set is \( [8, \infty) \) with an endpoint at 8 marked as closed.
• Shade to the right to indicate the solution for \( g \) values greater than or equal to 8.