Question

Which equation is equivalent to 4x+3+(-3x)+7-6x=11 ?

A. 8x + 3 = 11

B. 2x + 3 = 11

C. 5x = 11

D. -4x =11

Answer 1

To simplify the equation \( 4x + 3 + (-3x) + 7 - 6x = 11 \), we can combine like terms.

Starting with the equation:

\[
4x + 3 - 3x + 7 - 6x = 11
\]

Now, combine the coefficients of \( x \):

1. \( 4x - 3x - 6x = (4 - 3 - 6)x = -5x \)
2. Combine the constant terms: \( 3 + 7 = 10 \)

Now, rewrite the equation:

\[
-5x + 10 = 11
\]

Now, to isolate the terms involving \( x \), we subtract 10 from both sides:

\[
-5x = 11 - 10
\]
\[
-5x = 1
\]

None of the options directly match our form of \(-5x = 1\).

Let's go through the given options to find any equivalent forms:

- Option A: \( 8x + 3 = 11 \) does not match.
- Option B: \( 2x + 3 = 11 \) does not match.
- Option C: \( 5x = 11 \) does not match directly, but if we consider the factor of \(-1\) on both sides, we can equate \( -5x = -11 \).
- Option D: \(-4x = 11\) does not match.

Upon further inspection, it seems I have not matched any options correctly, as all the derived equations do not correlate with the provided options.

However, in solving \( -5x = 1 \), it can be rewritten as \( 5x = -1 \) (which is not in the options either).

Thus, the original equation simplifies to \( -5x + 10 = 11 \) which can help us find a value for \( x \), but does not correlate with the given multiple-choice answers.

After careful review, it seems there is no answer that matches directly derived from our simplified equation.