Solve the inequality and graph the solution.

Question

2(g–1)≥6
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 \( 2(g - 1) \geq 6 \), follow these steps:

1. Distribute the 2: \[ 2g - 2 \geq 6 \]

2. Add 2 to both sides: \[ 2g \geq 8 \]

3. Divide both sides by 2: \[ g \geq 4 \]

So the solution to the inequality is \( g \geq 4 \).

Graphing the solution:

1. Endpoints: The endpoint for \( g = 4 \) is included (since the inequality is greater than or equal to), so we plot this as a closed point at \( g = 4 \).

2. Ray: The solution also indicates that all values greater than 4 are part of the solution. We will represent this as a ray extending to the right from the point \( g = 4 \).

Final Graphic Representation:

• Plot a closed dot at \( g = 4 \) (indicating that 4 is included in the solution).
• Draw a ray extending to the right from this point, representing all values greater than 4.

Summary of the Graph:

• Closed dot on \( g = 4 \).
• Ray extending to the right (toward infinity).

This completes the solution of the inequality \( 2(g - 1) \geq 6 \).