https://file.aiquickdraw.com/mathbot/file/1729646263171emljqfyj.jpg

The inequality given in the image is:

\[
-2 \leq t \leq \frac{5}{9}
\]

### Step-by-step breakdown:
1. **Inequality**: The inequality states that the variable \( t \) is greater than or equal to \(-2\) and less than or equal to \( \frac{5}{9} \).
2. **Interval notation**: The solution set can be written as:
   \[
   [-2, \frac{5}{9}]
   \]
   This means that \( t \) can take any value between \(-2\) and \( \frac{5}{9} \), inclusive of the endpoints.
3. **Graphing**: On the number line:
   - Mark the points \(-2\) and \( \frac{5}{9} \).
   - Since the inequality includes both \(-2\) and \( \frac{5}{9} \) (indicated by the "less than or equal to" symbols), these points are closed circles.
   - Shade the region between \(-2\) and \( \frac{5}{9}\), indicating all values between them are part of the solution.

### Graph of the solution set:
- Closed circle at \( t = -2 \).
- Closed circle at \( t = \frac{5}{9} \) (which is slightly less than 1).
- The region between these points is shaded.

Does this explanation make sense to you? Would you like more details on graphing inequalities?

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Here are 5 related questions for practice:
1. How would you graph the solution to \( -1 \leq x < 3 \)?
2. Can you express \( -5 < x \leq 0 \) in interval notation?
3. What is the difference between a strict inequality and an inclusive inequality when graphing on a number line?
4. Solve and graph the inequality \( -3 \leq 2x + 1 < 4 \).
5. How do you handle inequalities that involve division by a negative number?

**Tip**: Always remember to flip the inequality sign when multiplying or dividing by a negative number.

Graph the solution set of the inequality -2 ≤ t ≤ 5/9.

Learn how to graph the solution set of the inequality -2 ≤ t ≤ 5/9 with a step-by-step explanation. This example covers fundamental algebra concepts, such as inequalities and number line graphing, suitable for students in Grades 6-8.

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