Question

In order to make the expression below equivalent to 1/2x + 6, which additional operation should be included in the expression?

5/4x + 6 + _

A. -x
B. 3/4x
C. -3/4x
D. -2x

Answer 1

To determine which additional operation should be included in the expression \( \frac{5}{4}x + 6 + \_ \) so that it equals \( \frac{1}{2}x + 6 \), we can set up the equation:

\[
\frac{5}{4}x + 6 + \_ = \frac{1}{2}x + 6
\]

Subtracting \( 6 \) from both sides gives us:

\[
\frac{5}{4}x + \_ = \frac{1}{2}x
\]

Next, we need to isolate the additional operation \( \_ \) by rearranging the equation:

\[
\_ = \frac{1}{2}x - \frac{5}{4}x
\]

To perform this subtraction, we need a common denominator, which will be \( 4 \):

\[
\frac{1}{2}x = \frac{2}{4}x
\]

Now we can substitute that back into the equation:

\[
\_ = \frac{2}{4}x - \frac{5}{4}x = \frac{2 - 5}{4}x = \frac{-3}{4}x
\]

Thus, the additional operation that should be included is \( -\frac{3}{4}x \).

The correct answer is:

C. \(-\frac{3}{4}x\)