Question

In order to make the expression below equivalent to 12x+6
, which additional operation should be included in the expression?

54x+6+
______

(1 point)
Responses

A.−2x
negative 2 x

B.−x
negative x

C.3/4 x
3 fourths x

D.−34x

Answers

GPT-4o mini
To make the expression \(54x + 6 + \_\_\_\_ \) equivalent to \(12x + 6\), we need to determine what value needs to be added to \(54x\) in order to get \(12x\).

1. Start with the equation:
\[
54x + \text{(unknown value)} = 12x
\]

2. Rearranging the equation to find the unknown value gives:
\[
\text{(unknown value)} = 12x - 54x
\]
\[
\text{(unknown value)} = -42x
\]

Now, we check which of the responses corresponds to \(-42x\):

A. \(-2x\)
B. \(-x\)
C. \(\frac{3}{4}x\)
D. \(-34x\)

None of the options given equal \(-42x\). It looks like there is no correct answer among the responses provided.

However, it seems \(D = -34x\) might have been expected to add to get a common number near -42. Using -34x alongside \(54x\) would yield:
\[
54x - 34x = 20x
\]
This still isn't correct.

Given none of the answers seem to work, we need an additional operation that equals -42, or review the problem options presented.

Thus, the appropriate additional operation to make \(54x + 6\) equivalent to \(12x + 6\) is to add \(-42x\) which doesn't match any option given.

Please let me know if you want to discuss further!
mav welborn
WHATS TGHE ANSWER
GPT-4o mini
To make the expression \(54x + 6 + \_\_\_\_\) equivalent to \(12x + 6\), we need to determine the value to add:

1. Start with the equation:
\[
54x + \text{(unknown value)} = 12x
\]

2. Rearranging gives:
\[
\text{(unknown value)} = 12x - 54x = -42x
\]

The options you provided are:
- A. \(-2x\)
- B. \(-x\)
- C. \(\frac{3}{4}x\)
- D. \(-34x\)

None of these options equal \(-42x\).

However, the option that subtracts the most from \(54x\) is \(D. -34x\).

If we take:
\[
54x - 34x = 20x
\]
It's still not equal to \(12x\), but it is the largest reduction.

Since none of the options achieve \(-42x\), if you need to select one, \(D. -34x\) would subtract the largest amount from \(54x\).

So if you must choose an answer from the options given, choose **D. -34x**, but note it won't get you to \(12x\). None of the choices match the necessary adjustment of \(-42x\) exactly.
mav welborn
WHATS THE CLOSEST ANSWER
GPT-4o mini
To determine the closest answer that gets \(54x + 6\) closer to \(12x + 6\), we can analyze how much we need to subtract from \(54x\) to bring it down to \(12x\).

We found that we need to subtract \(42x\) from \(54x\) to achieve this:

\[
54x - 42x = 12x
\]

Now, looking at your options:

- A. \(-2x\)
- B. \(-x\)
- C. \(\frac{3}{4}x\)
- D. \(-34x\)

The option that is closest to \(-42x\) is **D. \(-34x\)** because it removes a significant amount from \(54x\) (though still not enough to reach \(12x\)).

Thus, **choose D: -34x** as the closest answer provided.