Expand the following expression.

Question

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