Question

Solve the inequality and graph the solution.
2(g+4)+10<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 \( 2(g + 4) + 10 < 6 \), we will first simplify and isolate \( g \).

1. Distribute the \( 2 \):
\[
2g + 8 + 10 < 6
\]

2. Combine like terms:
\[
2g + 18 < 6
\]

3. Subtract \( 18 \) from both sides:
\[
2g < 6 - 18
\]
\[
2g < -12
\]

4. Divide both sides by \( 2 \):
\[
g < -6
\]

### Solution
The solution to the inequality is:
\[
g < -6
\]

### Graphing the Solution
To graph the solution \( g < -6 \):

1. **Identify the endpoints**: The endpoint is \( -6 \).
2. **Select an endpoint to change it from closed to open**: Since \( g < -6 \) does not include \( -6 \), we will represent it as an open circle at \( -6 \).
3. **Select the middle of the segment, ray, or line to delete it**: Since the solution is \( g < -6 \), we will shade to the left (in the negative direction) of \( -6 \).

### Final Graph
- Place an open circle at \( -6 \) to indicate that it is not included in the solution.
- Shade everything to the left of \( -6 \) to represent all values that are less than \( -6 \).

The graph will look like this:

\[
\text{---o-------------------}
-7 -6 -5
\]

Where "o" is an open circle representing \( -6 \) and the shading extends to all values left of \( -6 \).