Question

Solve the inequality and graph the solution.
3(u–10)+18≤12
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 \( 3(u - 10) + 18 \leq 12 \), we can follow these steps:

1. **Distribute and simplify the left side:**
\[
3(u - 10) + 18 \leq 12
\]
\[
3u - 30 + 18 \leq 12
\]
\[
3u - 12 \leq 12
\]

2. **Add 12 to both sides:**
\[
3u \leq 24
\]

3. **Divide by 3:**
\[
u \leq 8
\]

The solution set is \( u \leq 8 \).

### Graphing the Solution:
- The solution \( u \leq 8 \) includes all numbers less than or equal to 8.
- We will represent this on a number line.

### Steps to graph:
1. **Draw a number line.**
2. **Plot the point at 8.** Since the inequality is less than or equal to (≤), we use a closed dot at 8.
3. **Shade to the left of 8**, indicating all values less than 8 are included in the solution.

### Change from Closed to Open:
- If asked to change an endpoint from closed to open, we can modify it to \( u < 8 \) instead of \( u \leq 8 \) (this means moving from a closed dot to an open dot).
- Therefore, instead of shading up to and including 8, we would leave it out with an open dot.

### Deleting the Middle of the Segment:
- You would keep all the shaded region to the left but ensure not to include the endpoint at 8, effectively marking it open.

Thus, the final graphical representation would have:
- An open dot at 8.
- Shading extending infinitely to the left towards negative infinity.

### Final Answer:
- **Solution**: \( u \leq 8 \) (or \( u < 8 \) if changing to open).
- **Graph**: Closed dot at 8 (if original) or open dot at 8 (if changed), with shading to the left.