https://file.aiquickdraw.com/mathbot/file/1726178252105czi7xrtj.jpg

The equation given in the image is:

\[
| -a + 2 | + 9 = 6
\]

### Step-by-step solution:

1. **Isolate the absolute value term:**

   Subtract 9 from both sides to isolate the absolute value expression:
   
   \[
   | -a + 2 | = 6 - 9
   \]
   
   Simplifying the right side:
   
   \[
   | -a + 2 | = -3
   \]
   
2. **Interpret the absolute value:**

   The absolute value of any expression is always non-negative. This means that \( | -a + 2 | \geq 0 \). 
   
   Since \( -3 \) is negative, there is no solution to this equation because an absolute value cannot equal a negative number.

### Conclusion:

There is **no solution** to this equation.

---

Would you like more details, or do you have any questions?

Here are five related questions for further practice:

1. How do you solve an absolute value equation when the result is positive?
2. What is the general approach to solving equations involving absolute values?
3. How would you solve \( |x + 5| = 3 \)?
4. What happens when the absolute value is set equal to zero?
5. How can you graph absolute value equations?

**Tip:** Always check if the result of an absolute value equation can logically exist (it must be non-negative).

This guide explains how to solve the absolute value equation | -a + 2 | + 9 = 6, providing a step-by-step approach. It covers key algebraic concepts, such as isolating the absolute value term and the properties of absolute value. Suitable for students in Grades 8-10.

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