Simplify 5/8x + 1/2 (1/4x+10) Write your fractions in simplest form.

1 answer

To simplify the expression \( \frac{5}{8}x + \frac{1}{2} \left(\frac{1}{4}x + 10\right) \), let's start by distributing \( \frac{1}{2} \) across the expression inside the parentheses.

\[ \frac{1}{2} \left( \frac{1}{4}x + 10 \right) = \frac{1}{2} \cdot \frac{1}{4}x + \frac{1}{2} \cdot 10 \] \[ = \frac{1}{8}x + 5 \]

Now, we can substitute this back into the original expression:

\[ \frac{5}{8}x + \left(\frac{1}{8}x + 5\right) \]

Next, we can combine the terms containing \( x \):

\[ \frac{5}{8}x + \frac{1}{8}x = \left(\frac{5}{8} + \frac{1}{8}\right)x = \frac{6}{8}x \]

Now, simplify \( \frac{6}{8} \):

\[ \frac{6}{8} = \frac{3}{4} \]

Thus, we have:

\[ \frac{3}{4}x + 5 \]

So, the final simplified expression is:

\[ \frac{3}{4}x + 5 \]