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(1)/(6)x +(3)/(4)((1)/(2) x - 4)

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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:

\(\frac{13}{24}x - 3\)

User Teemu
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