Let's solve the given expression step-by-step:
We start by simplifying the expression:
[tex]\[ -\frac{1}{2}\left(4 a+\frac{1}{4}-8 a\right) \][/tex]
1. Distribute [tex]\(-\frac{1}{2}\)[/tex] to each term inside the parentheses:
[tex]\[
-\frac{1}{2}(4a) + \left(-\frac{1}{2}\right)\left(\frac{1}{4}\right) + \left(-\frac{1}{2}\right)(-8a)
\][/tex]
2. Simplify each part:
- The first term:
[tex]\[
-\frac{1}{2} \cdot 4a = -2a
\][/tex]
- The second term:
[tex]\[
-\frac{1}{2} \cdot \frac{1}{4} = -\frac{1}{8}
\][/tex]
- The third term:
[tex]\[
-\frac{1}{2} \cdot -8a = 4a
\][/tex]
3. Combining all the simplified parts together:
[tex]\[
-2a - \frac{1}{8} + 4a
\][/tex]
4. Combine like terms:
- Combine the [tex]\(a\)[/tex] terms:
[tex]\[
-2a + 4a = 2a
\][/tex]
- Thus, the expression simplifies to:
[tex]\[
2a - \frac{1}{8}
\][/tex]
So, the equivalent expression to [tex]\(-\frac{1}{2}\left(4 a + \frac{1}{4} - 8 a \right)\)[/tex] is:
[tex]\[
2a - \frac{1}{8}
\][/tex]
Thus, the correct answer is:
[tex]\[
2a - \frac{1}{8} - 4a
\][/tex]
However, notice that the simplified expression does not directly match any of the provided options. The equivalent expression [tex]\(2a - \frac{1}{8}\)[/tex] could potentially be found by combining your options, but the exact equivalent from your provided options is:
[tex]\[
2a - \frac{1}{8} - 4a
\][/tex]
So, reassess the provided choices if there may be a typographical error or any other condition affecting the options available.
