https://file.aiquickdraw.com/mathbot/file/1726495299740tugtbe64.jpg

The problem on the screen is an absolute value equation:

\[
| -9 + a | = 1
\]

### To solve for \( a \), follow these steps:

1. The definition of absolute value tells us that:
   \[
   |x| = 1 \quad \text{means} \quad x = 1 \quad \text{or} \quad x = -1.
   \]

2. Apply this to the equation:
   \[
   -9 + a = 1 \quad \text{or} \quad -9 + a = -1.
   \]

#### Case 1:
\[
-9 + a = 1
\]
Solve for \( a \):
\[
a = 1 + 9 = 10.
\]

#### Case 2:
\[
-9 + a = -1
\]
Solve for \( a \):
\[
a = -1 + 9 = 8.
\]

### Therefore, the solutions are:
\[
a = 10 \quad \text{or} \quad a = 8.
\]

Do you want any further details or have any questions?

### Related questions:
1. How do we solve more complex absolute value equations?
2. What happens if the equation has no solutions?
3. Can an absolute value equation have more than two solutions?
4. What if the absolute value is set to a negative number, like \( |-9 + a| = -1 \)?
5. How do we graph the solution of this absolute value equation?

**Tip:** Always isolate the absolute value part of the equation before solving.

|-9 + a| = 1. Solve for all values of a in simplest form.

Learn how to solve the absolute value equation |-9 + a| = 1 with a clear step-by-step solution. This problem involves absolute value properties and algebraic manipulation, suitable for students in Grades 6-8.

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