Question

Solve the inequality and graph the solution.
–
20≥10(t+1)
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

which way would it be shaded

Answer 2

To solve the inequality \(-20 \geq 10(t + 1)\), we can begin by isolating \(t\).

1. Distribute the 10:

\[
-20 \geq 10t + 10
\]

2. Subtract 10 from both sides:

\[
-20 - 10 \geq 10t
\]
\[
-30 \geq 10t
\]

3. Divide both sides by 10 (remember that dividing by a positive number does not change the direction of the inequality):

\[
-3 \geq t
\]

This can be rewritten as:

\[
t \leq -3
\]

Now, we can graph the solution \(t \leq -3\).

### Graphing:

1. **Endpoints**: The endpoint is \(-3\).
2. **Open or Closed**: Since the inequality is less than or equal to (≤), we use a closed dot at \(-3\).
3. **Direction**: Since \(t\) can take any value less than or equal to \(-3\), we shade to the left (toward negative infinity).

### Representation:
- The position of \(-3\) is marked with a closed dot, indicating that it is included in the solution set.
- The shaded line extending to the left indicates all values less than \(-3\).

**Final Representation**:

- The graph would show a closed dot at \(-3\) and a line extending to the left, indicating all values of \(t\) that satisfy the inequality.

If you have any further requests or need a visual reference, please let me know!