To solve the inequality \( 85 \leq 17(g - 3) \), we can start by isolating \( g \).
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Distribute the 17 on the right side: \[ 85 \leq 17g - 51 \]
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Add 51 to both sides: \[ 85 + 51 \leq 17g \] \[ 136 \leq 17g \]
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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.