To simplify the expression \(-\frac{1}{2}(-3y + 10)\), we need to distribute the \(-\frac{1}{2}\) across the terms inside the parentheses.

### Step-by-step:

1. Distribute \(-\frac{1}{2}\) to each term:
   \[
   -\frac{1}{2} \times (-3y) + -\frac{1}{2} \times 10
   \]

2. Simplify each multiplication:
   \[
   (-\frac{1}{2} \times -3y) = \frac{3y}{2}
   \]
   \[
   (-\frac{1}{2} \times 10) = -5
   \]

3. Combine the simplified terms:
   \[
   \frac{3y}{2} - 5
   \]

So, the simplified expression is:
\[
\frac{3y}{2} - 5
\]

Would you like more details on any part of this solution?

Here are some related questions to expand your understanding:

1. How would you solve an equation involving this expression?
2. What happens if the expression inside the parentheses changes?
3. Can you factor out common terms in this expression?
4. How do you solve for \(y\) if given \(\frac{3y}{2} - 5 = 0\)?
5. How would the expression change if you had a different fraction multiplier?

**Tip:** When simplifying expressions, always distribute carefully to avoid sign errors.

Learn how to simplify the algebraic expression -1/2(-3y + 10) using the distributive property. This step-by-step solution covers key algebraic concepts, including distributing a negative fraction and simplifying the resulting terms. Suitable for students in Grades 6-8.

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