In order to make the expression below equivalent to 1/2x+6

Question

, which additional operation should be included in the expression?

5/4x+6+ ______

(1 point)
Responses

−3/4x
negative 3 fourths x

−x
negative x

−2x
negative 2 x

3/4x

Answer 1

To make the expression \( \frac{5}{4}x + 6 + ___ \) equivalent to \( \frac{1}{2}x + 6 \), we need to determine what to add to \( \frac{5}{4}x \).

First, let's rewrite \( \frac{1}{2}x \) so that it has a common denominator with \( \frac{5}{4}x \). The common denominator is 4:

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

Now we want to find the value that we need to add to \( \frac{5}{4}x \) to get \( \frac{2}{4}x \):

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

Subtracting \( \frac{5}{4}x \) from both sides:

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

Thus, the additional operation to make the expression equivalent to \( \frac{1}{2}x + 6 \) is:

\[ -\frac{3}{4}x \]

So the correct response is:

−3/4x