Solve the inequality and graph the solution.

Question

4g–
2
5
(5g–10)≥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 \(4g - \frac{2}{5}(5g - 10) \geq 10\), we will first simplify the left-hand side.

1. Distribute \(-\frac{2}{5}\) to the expression inside the parentheses: \[ -\frac{2}{5}(5g - 10) = -\frac{2}{5} \cdot 5g + \frac{2}{5} \cdot 10 = -2g + 4. \]

2. Substitute this back into the inequality: \[ 4g - 2g + 4 \geq 10. \]

3. Combine like terms: \[ 2g + 4 \geq 10. \]

4. Isolate the variable \(g\): \[ 2g \geq 10 - 4, \] \[ 2g \geq 6. \]

5. Divide by 2: \[ g \geq 3. \]

Now we have our solution: \(g \geq 3\).

Graphing the Solution

To graph the solution, we do the following:

• Plot the endpoint at \(g = 3\). Since \(g\) is greater than or equal to 3, we will use a closed dot at \(g = 3\) to indicate that 3 is included in the solution.
• Shade to the right of \(g = 3\) to represent all values greater than 3.

Steps to Graph:

1. Plot a closed dot at \(3\).
2. Shade the region to the right of \(3\).

Changing from Closed to Open

If we need to change the dot from closed to open for endpoints, the endpoint at \(g = 3\) could be changed to an open dot, indicating that \(g\) does not include \(3\). But in this inequality \(g \geq 3\), the closed dot is appropriate since 3 is included in the solution.

So, the correct graphing representation is:

• Closed dot at \(g = 3\).
• Shade the line to the right representing \(g > 3\).

Final Note

In summary, the solution \(g \geq 3\) includes the value \(3\), so we keep the closed dot there in the graph. The graphical representation would show all numbers starting from \(3\) and extending to infinity in the right direction.