We are given the equation:

\[
13 = |y + 28|
\]

To solve this, we need to account for the fact that the absolute value \( |x| \) has two cases:

1. \( x \) if \( x \geq 0 \)
2. \( -x \) if \( x < 0 \)

Therefore, we will consider two possible cases for the expression inside the absolute value:

### Case 1: \( y + 28 = 13 \)

\[
y + 28 = 13
\]

Subtract 28 from both sides:

\[
y = 13 - 28
\]

\[
y = -15
\]

### Case 2: \( y + 28 = -13 \)

\[
y + 28 = -13
\]

Subtract 28 from both sides:

\[
y = -13 - 28
\]

\[
y = -41
\]

### Solution:
The two possible solutions for \( y \) are:

\[
y = -15 \quad \text{or} \quad y = -41
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. What happens if you have a negative value outside the absolute value?
2. How do you graph absolute value equations?
3. Can absolute value inequalities be solved similarly?
4. How do absolute value equations relate to real-world problems?
5. What if the number on the right side of the equation is negative?

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios.

Learn how to solve the absolute value equation 13 = |y + 28| with a detailed step-by-step solution. This algebra problem covers key concepts like absolute value and includes two possible solutions: y = -15 and y = -41. Suitable for students in Grades 7-9.

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