To solve the equation 

\[
36 = |6 - 5y|,
\]

we need to consider the two possible cases for the absolute value expression. Recall that the absolute value function, \( |x| \), outputs the non-negative value of \( x \). Therefore, \( |6 - 5y| = 36 \) implies two cases:

1. **Case 1:** \(6 - 5y = 36\)
2. **Case 2:** \(6 - 5y = -36\)

Let's solve each case separately.

### Case 1: \(6 - 5y = 36\)

\[
6 - 5y = 36
\]

Subtract 6 from both sides:

\[
-5y = 36 - 6
\]

\[
-5y = 30
\]

Divide both sides by -5:

\[
y = \frac{30}{-5}
\]

\[
y = -6
\]

### Case 2: \(6 - 5y = -36\)

\[
6 - 5y = -36
\]

Subtract 6 from both sides:

\[
-5y = -36 - 6
\]

\[
-5y = -42
\]

Divide both sides by -5:

\[
y = \frac{-42}{-5}
\]

\[
y = 8.4
\]

### Solutions

The two solutions for \( y \) are:

\[
y = -6 \quad \text{and} \quad y = 8.4
\]

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

Here are some related questions:

1. What is the general procedure for solving equations with absolute values?
2. How do absolute value equations differ from absolute value inequalities?
3. Can absolute value equations have more than two solutions?
4. How do we graph absolute value functions?
5. What are some real-world applications of absolute value equations?

**Tip:** Always consider both the positive and negative scenarios when dealing with absolute value equations.

Learn how to solve the absolute value equation |6 - 5y| = 36 step-by-step with detailed solutions. Understand the concept of absolute value equations and find the solutions for y. Suitable for high school students (Grades 9-12).

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