Solve the inequality and graph the solution.

Question

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 \( -6 \).