To solve the equation \(23y + 13 = -5y + 21\), let's follow these steps:

1. **Combine like terms by adding \(5y\) to both sides**:
   \[
   23y + 5y + 13 = 21
   \]
   Simplifies to:
   \[
   28y + 13 = 21
   \]

2. **Subtract 13 from both sides**:
   \[
   28y = 21 - 13
   \]
   Simplifies to:
   \[
   28y = 8
   \]

3. **Divide both sides by 28**:
   \[
   y = \frac{8}{28}
   \]
   Simplifies to:
   \[
   y = \frac{2}{7}
   \]

So, the solution is \( y = \frac{2}{7} \).

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

Here are some related questions you might find interesting:
1. How do you solve equations with variables on both sides?
2. What happens if you have fractions in equations?
3. How can you check if your solution is correct?
4. What is the process to simplify fractions?
5. How do you solve equations with multiple steps?

**Tip:** Always perform the same operation on both sides of an equation to keep it balanced!

Learn how to solve the equation 23y + 13 = -5y + 21 with a detailed step-by-step solution. This problem involves solving linear equations and includes combining like terms, simplifying expressions, and solving for the variable. Suitable for students in Grades 7-9.

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