https://file.aiquickdraw.com/mathbot/file/1726166457103ull2t0ms.jpg

The inequality shown in the image is:

\[
20t + 8,500 \geq 17,000
\]

Let's solve this inequality for \( t \).

### Step 1: Subtract 8,500 from both sides
\[
20t \geq 17,000 - 8,500
\]
\[
20t \geq 8,500
\]

### Step 2: Divide both sides by 20
\[
t \geq \frac{8,500}{20}
\]
\[
t \geq 425
\]

### Interval Notation:
The solution in interval notation is:
\[
[425, \infty)
\]

This means that \( t \) must be greater than or equal to 425.

Would you like further details, or have any questions?

Here are some follow-up questions:
1. How do we interpret interval notation in the context of inequalities?
2. What happens if the inequality sign is reversed (e.g., \( \leq \) instead of \( \geq \))?
3. What is the difference between a strict inequality (\( > \)) and a non-strict inequality (\( \geq \))?
4. How would the solution change if the inequality had a negative coefficient for \( t \)?
5. What real-world situations can be modeled by inequalities?

**Tip:** Always check your final solution by substituting values back into the original inequality to verify they satisfy the condition.

Solve the inequality: 20t + 8,500 ≥ 17,000. Provide the solution in interval notation.

Learn how to solve the linear inequality 20t + 8,500 ≥ 17,000 step by step. This guide explains the method of solving inequalities and converting the solution into interval notation. Suitable for Grades 7-9 students.

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