Solve the inequality and graph the solution.

Question

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.