The equation you provided is:

$\frac{|y - 10|}{-2} = -6$

Let's solve this step by step:

Step 1: Multiply both sides by $-2$

To eliminate the denominator, multiply both sides of the equation by $-2$:

$|y - 10| = (-6) \times (-2)$

This simplifies to:

$|y - 10| = 12$

Step 2: Solve the absolute value equation

The absolute value equation $|y - 10| = 12$ implies two cases:

1. $y - 10 = 12$
2. $y - 10 = -12$

Step 3: Solve both cases

• For the first case: $y - 10 = 12$

$y = 12 + 10$ $y = 22$

• For the second case: $y - 10 = -12$

$y = -12 + 10$ $y = -2$

Final Solution:

The two possible solutions for $y$ are: $y = 22 \quad \text{or} \quad y = -2$

Would you like further details on any part of the process? Here are a few related questions:

1. How do you handle more complex absolute value equations?
2. What happens when the equation involves multiple absolute values?
3. How do you check if your solutions are correct in absolute value problems?
4. What if the equation had no real solutions? How would you handle that case?
5. What are the graphical interpretations of absolute value equations?

Tip: Always check both possible solutions when solving absolute value equations to ensure completeness.