Final answer:
To simplify the expression \(\frac{1}{6}x +\frac{3}{4}(\frac{1}{2} x - 4)\), distribute the \(\frac{3}{4}\) and combine like terms, resulting in \(\frac{13}{24}x - 3\).
Step-by-step explanation:
We need to simplify the given expression:
\(\frac{1}{6}x +\frac{3}{4}(\frac{1}{2}x - 4)\)
To start, distribute the \(\frac{3}{4}\) across the parentheses:
\(\frac{1}{6}x + \frac{3}{4} \cdot \frac{1}{2}x - \frac{3}{4} \cdot 4\)
Do the multiplication:
\(\frac{1}{6}x + \frac{3}{8}x - 3\)
Add the x terms:
\(\frac{1}{6}x + \frac{3}{8}x = \frac{4}{24}x + \frac{9}{24}x = \frac{13}{24}x\)
Now, we have: \(\frac{13}{24}x - 3\)
The original expression simplifies to:
\(\frac{13}{24}x - 3\)