Question

Multiple Choice Question
Which expression is NOT equivalent to 9x + 4y + 13 - 3x -y -10?

A. 3(2x + y + 1)

B. 6x + 3(1 + y)

C. (9 - 3)x + (4 - 0)y + 3

D. (13 - 10) + (9x - 3x) + (4y - y)

Answer 1

To determine which expression is NOT equivalent to \(9x + 4y + 13 - 3x - y - 10\), we first simplify the original expression.

Combine like terms:

\[
9x - 3x + 4y - y + 13 - 10
\]

This simplifies to:

\[
(9 - 3)x + (4 - 1)y + (13 - 10) = 6x + 3y + 3
\]

Now we'll simplify each of the options to see which one is not equivalent to \(6x + 3y + 3\).

**Option A: \(3(2x + y + 1)\)**

Distributing the 3 gives:

\[
3 \cdot 2x + 3 \cdot y + 3 \cdot 1 = 6x + 3y + 3
\]

**Option B: \(6x + 3(1 + y)\)**

Distributing the 3 gives:

\[
6x + 3 \cdot 1 + 3 \cdot y = 6x + 3 + 3y
\]

This is also \(6x + 3y + 3\).

**Option C: \((9 - 3)x + (4 - 0)y + 3\)**

Simplifying gives:

\[
6x + 4y + 3
\]

This is **NOT** equivalent since we have \(6x + 4y + 3\) instead of \(6x + 3y + 3\).

**Option D: \((13 - 10) + (9x - 3x) + (4y - y)\)**

Calculating each term gives:

\[
3 + 6x + 3y
\]

This is equivalent to \(6x + 3y + 3\).

Thus, the expression that is NOT equivalent to \(9x + 4y + 13 - 3x - y - 10\) is:

**C. \((9 - 3)x + (4 - 0)y + 3\)**