Question

Solve the inequality and graph the solution.
10(d+6)–10≤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:

1. Start with the inequality:
\[
10(d + 6) - 10 \leq 10
\]

2. Distribute the 10 on the left side:
\[
10d + 60 - 10 \leq 10
\]
Simplifying gives:
\[
10d + 50 \leq 10
\]

3. Subtract 50 from both sides:
\[
10d \leq 10 - 50
\]
Simplifying gives:
\[
10d \leq -40
\]

4. Divide both sides by 10:
\[
d \leq -4
\]

The solution to the inequality is:
\[
d \leq -4
\]

### Graphing the Solution

To graph this solution on a number line:

1. Plot the point at \(-4\).
2. Since the inequality is \(d \leq -4\), we will use a closed dot at \(-4\) (indicating that \(-4\) is included in the solution).
3. Shade to the left of \(-4\) to indicate that all numbers less than \(-4\) are included in the solution.

### Changing the Endpoint and Deleting a Segment

1. **Change from closed to open**: Let's change the endpoint from closed to open. So, we will make the dot at \(-4\) open, indicating that \(-4\) is not included in the solution.

2. To fulfill the instruction to delete the middle of the segment, let's say we delete the segment starting from the open dot at \(-4\) extending to the left since our solution is \((-\infty, -4)\) without including \(-4\).

Thus, the final graph will be:

- An **open circle** at \(-4\).
- Shaded to the left towards negative infinity, indicating that all values less than \(-4\) are part of the solution, but \(-4\) itself is not included.

This reflects the solution \(d < -4\) in a visual manner.