Question

In order to make the expression below equivalent to Ex + 6, which additional operation should be included in the expression?
5/4x + 6+___
(1 point)
-x
3/4x
-3/4x
-2x

Answer 1

To make the expression \( \frac{5}{4}x + 6 + \_\_\_ \) equivalent to \( Ex + 6 \), we want to find an operation that modifies the coefficient of \( x \) in the expression \( \frac{5}{4}x + 6 \) to be equal to the coefficient \( E \) in the expression \( Ex + 6 \).

Let's compare the two expressions without the constant \( 6 \):

We have:
\[
\frac{5}{4}x + \_\_ = Ex
\]

To isolate the unknown, we rearrange it:
\[
\_\_ = Ex - \frac{5}{4}x
\]

Factoring \( x \) out:
\[
\_\_ = (E - \frac{5}{4})x
\]

Now, if we want to include an operation that involves \( x \), we can analyze the provided options. We're looking for a term that effectively reduces the \( \frac{5}{4}x \) to \( Ex \).

Let's evaluate the provided options:

1. **\(-x\)**:
\[
\frac{5}{4}x - x = \frac{5}{4}x - \frac{4}{4}x = \frac{1}{4}x
\]
Here, \( E = \frac{1}{4} \).

2. **\(\frac{3}{4}x\)**:
\[
\frac{5}{4}x + \frac{3}{4}x = \frac{8}{4}x = 2x
\]
Here, \( E = 2 \).

3. **\(-\frac{3}{4}x\)**:
\[
\frac{5}{4}x - \frac{3}{4}x = \frac{2}{4}x = \frac{1}{2}x
\]
Here, \( E = \frac{1}{2} \).

4. **\(-2x\)**:
\[
\frac{5}{4}x - 2x = \frac{5}{4}x - \frac{8}{4}x = -\frac{3}{4}x
\]
Here, \( E = -\frac{3}{4} \).

Each option gives a different coefficient for \( x \). So, the choice that will align the expression such that it simplifies to \( Ex + 6 \) depends on the exact target value of \( E \).

To get the expression \( \frac{5}{4}x + 6 + \_\_ \) equivalent to \( Ex + 6 \), the correct option should reduce \( \frac{5}{4} \) to zero.

If we calculate further, **the correct option that would make it equivalent to \( 0x + 6 \)** (i.e., no \( x \) term):

Thus, the best choice is:
\[
-\frac{5}{4}x \implies \text{which is equivalent to } -x \text{ is the most appropriate choice to make coefficient vanish.}
\]

The answer is: **\(-x\)**.