Question

Solve the inequality and graph the solution.
2(b+6)+6<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

Let's solve the inequality step by step.

Given the inequality:
\[
2(b + 6) + 6 < 10
\]

First, distribute the \(2\):
\[
2b + 12 + 6 < 10
\]
Combine like terms:
\[
2b + 18 < 10
\]

Next, subtract \(18\) from both sides:
\[
2b < 10 - 18
\]
\[
2b < -8
\]

Now, divide both sides by \(2\):
\[
b < -4
\]

The solution to the inequality is:
\[
b < -4
\]

### Graphing the solution:

1. **Endpoints**: The endpoint is \(-4\).
2. **Open/Closed endpoint**: Since the inequality is strictly less than (\(<\)), we will use an open circle at \(-4\).
3. **Middle of segment**: The solution is a ray going to the left from \(-4\).

### Final Graph:

On a number line:
- Place an open circle at \(-4\).
- Shade to the left to indicate that all values less than \(-4\) are part of the solution.

The graph looks like this:

```
<---( -4 )--------------------------------------------------->
```

Here, the open circle at \(-4\) indicates that \(-4\) itself is not included in the solution. The shaded area to the left signifies all numbers less than \(-4\) are included in the solution.