https://file.aiquickdraw.com/mathbot/file/1726068893271farvz5mq.jpg

The image contains algebraic problems, specifically focusing on absolute value equations and problem-solving involving ranges of temperatures for tropical fish.

Here’s a breakdown of the key tasks shown:

### Evaluating Expressions:
1. \( |x - 8| \) for \( x = -4 \)
2. \( 2|y| \) for \( y = -9 \)
3. \( -3|y| \) for \( y = -9 \)
4. \( -2|3x + 8| - 4 \) for \( x = -4 \)

### Problem-Solving:
**5. Tropical Fish Problem**
- **a.** Determine an equation for optimal water temperatures (range of 2°F from 76°F to 78°F).
- **b.** Solve the equation from part **a**.
- **c.** Discuss temperature accuracy and maintaining minimum temperature with thermometer accuracy of ±1°F.

### Solving Absolute Value Equations:
6. \( |x + 8| = 12 \)
7. \( |4 - 9x| = 11 \)
8. \( |x - 5| + 4 = 9 \)
9. \( |3x - 5| - 4 = 8 \)
10. \( |2x - 3| = 5 \)
11. \( |4 - 3x| = 6 \)
12. \( |4 - 3x| = 6 \)

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I can help solve any of these problems if you'd like. Let me know which one you'd like to start with, or if you'd like assistance with all of them!

### Follow-Up Questions:
1. How do you solve an absolute value equation?
2. What is the range of solutions for \( |x| = a \)?
3. How do you approach solving for temperature ranges in the tropical fish problem?
4. What role does the accuracy of a thermometer play in maintaining water temperature?
5. Can an absolute value equation have no solution? Under what conditions?

### Tip:
When solving absolute value equations, remember that the equation \( |A| = B \) translates to two cases: \( A = B \) and \( A = -B \).

Solve absolute value equations and solve the problem involving tropical fish temperature ranges.

Learn how to solve absolute value equations, such as |x + 8| = 12, and tackle a real-world tropical fish tank problem. This includes determining optimal temperature ranges for fish survival within a margin of error. Suitable for Grades 8-10.

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