Question

Expand the following expression.
9/4(5x+3/4)
a. 45/4x+27/16
b.9/4x+27/16
c.10x+9/16
d.45/4x+27/4

Answer 1

To expand the expression \(\frac{9}{4}(5x + \frac{3}{4})\), we apply the distributive property:

\[
\frac{9}{4}(5x) + \frac{9}{4}\left(\frac{3}{4}\right)
\]

Calculating each term:

1. For the first term:
\[
\frac{9}{4} \cdot 5x = \frac{45}{4}x
\]

2. For the second term:
\[
\frac{9}{4} \cdot \frac{3}{4} = \frac{27}{16}
\]

Now, combine both terms:

\[
\frac{45}{4}x + \frac{27}{16}
\]

Thus, the expanded expression is:

\[
\frac{45}{4}x + \frac{27}{16}
\]

So the correct answer is:

**a. \(\frac{45}{4}x + \frac{27}{16}\)**.