Question

Solve the inequality and graph the solution.
10≥3(k+8)–8
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 \( 10 \geq 3(k + 8) - 8 \), we first simplify the expression on the right side.

1. Distribute the 3:
\[
10 \geq 3k + 24 - 8
\]
This simplifies to:
\[
10 \geq 3k + 16
\]

2. Next, we isolate \( k \) by subtracting 16 from both sides:
\[
10 - 16 \geq 3k
\]
This simplifies to:
\[
-6 \geq 3k
\]

3. Now, divide both sides by 3 to solve for \( k \):
\[
-2 \geq k
\]
or equivalently,
\[
k \leq -2
\]

The solution to the inequality is \( k \leq -2 \).

### Graphing the Solution:

1. **Endpoints**: The endpoint here is \( k = -2 \).

2. **Choosing Closed or Open**: Since the inequality is \( \leq \), we plot the endpoint at \( -2 \) as a closed point (solid dot).

3. **Deleting Segment**: Since \( k \) is less than or equal to \( -2 \), we draw a solid line extending to the left from the closed point at \( -2 \) to indicate all values less than \( -2 \).

### Final Graph Representation:
- A solid dot at \( -2 \).
- A line extending to the left towards negative infinity.

In a graphical representation:
- A solid point at \( -2 \) represents that \( -2 \) is included in the solution.
- An arrow extending indefinitely to the left represents all values less than \( -2 \).

If you were to visualize it on a number line:
```
<----●========>
-2
```
Where:
- \( -2 \) is closed (included).
- The line extends indefinitely to the left.