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To factor out \(-\frac{1}{2}\) from the expression \(-\frac{1}{2}x + 6\), let's proceed as follows:

1. Start with the expression:
   \[
   -\frac{1}{2}x + 6
   \]

2. Factor out \(-\frac{1}{2}\):
   \[
   -\frac{1}{2} \left( x - 12 \right)
   \]

### Explanation:
When we factor out \(-\frac{1}{2}\), we are essentially dividing each term by \(-\frac{1}{2}\). Here's the breakdown:

- \(-\frac{1}{2}x\) divided by \(-\frac{1}{2}\) gives \(x\).
- \(6\) divided by \(-\frac{1}{2}\) gives \(-12\).

Thus, the factored form is:
\[
-\frac{1}{2} \left( x - 12 \right)
\]

Would you like a more detailed breakdown, or do you have any questions?

### Related Questions
1. How do you factor out constants from an expression with multiple terms?
2. What is the purpose of factoring out a term from an algebraic expression?
3. How do you handle negative signs when factoring terms in algebra?
4. How can factoring be used to simplify expressions in calculus?
5. What are some common mistakes to avoid when factoring expressions?

### Tip
When factoring out fractions, think of it as dividing each term by the fraction, and remember that dividing by a negative fraction will change the signs.

Factor \(-\frac{1}{2}\) out of \(-\frac{1}{2}x + 6\).

Understand how to factor out \(-\frac{1}{2}\) from the expression \(-\frac{1}{2}x + 6\) with a detailed solution. This problem covers key algebra concepts, including factoring constants from linear expressions. Suitable for students in Grade 8.

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