Solve the inequality and graph the solution.

Question

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9<3(g–7)
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 \(-9 < 3(g - 7)\), follow these steps:

1. Distribute the 3: \[ -9 < 3g - 21 \]

2. Add 21 to both sides: \[ -9 + 21 < 3g \] \[ 12 < 3g \]

3. Divide both sides by 3: \[ \frac{12}{3} < g \] \[ 4 < g \] This can also be written as: \[ g > 4 \]

Graphing the solution:

To graph \(g > 4\):

• Endpoint at 4: Use an open circle at 4 to indicate that 4 is not included in the solution.
• Shade to the right: This shows that all values greater than 4 are included in the solution.

Summary of the graph:

• The point at \(g = 4\) is an open circle.
• Shade the region to the right of the point to indicate all values greater than 4.

The final graph looks like this:

<---o-------------------->
      4

Where the open circle at 4 indicates that the value is not included in the solution.