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

is that correct

Answer 2

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

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

Combining like terms:

1. Combine the \( x \) terms:
\[
9x - 3x = 6x
\]

2. Combine the \( y \) terms:
\[
4y - y = 3y
\]

3. Combine the constant terms:
\[
13 - 10 = 3
\]

Putting it all together, we get:
\[
6x + 3y + 3
\]

Now, we will evaluate each of the provided options to see if they simplify to \( 6x + 3y + 3 \).

**A. \( 3(2x+y+1) \)**

\[
3(2x + y + 1) = 3 \times 2x + 3 \times y + 3 \times 1 = 6x + 3y + 3
\]

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

**B. \( 6x + 3(1+y) \)**

\[
6x + 3(1+y) = 6x + 3 \times 1 + 3 \times y = 6x + 3 + 3y
\]
This is equivalent to \( 6x + 3y + 3 \).

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

\[
(9-3)x + (4-0)y + 3 = 6x + 4y + 3
\]

This is NOT equivalent to \( 6x + 3y + 3 \) (since the y-coefficient is different).

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

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

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

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

\[
\boxed{C}
\]

Answer 3

Let's go through the problem step-by-step again to ensure we are correct.

We start with the expression:

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

**Step 1: Simplify the expression.**

1. Combine like terms for \(x\):
\[
9x - 3x = 6x
\]

2. Combine like terms for \(y\):
\[
4y - y = 3y
\]

3. Combine constant terms:
\[
13 - 10 = 3
\]

Putting it all together, we have:
\[
6x + 3y + 3
\]

Now we'll examine the choices A, B, C, and D to see if they simplify to \(6x + 3y + 3\).

**Option A: \(3(2x+y+1)\)**
\[
3(2x + y + 1) = 3 \times 2x + 3 \times y + 3 \times 1 = 6x + 3y + 3
\]
**Equivalent**

---

**Option B: \(6x + 3(1+y)\)**
\[
6x + 3(1+y) = 6x + 3 \times 1 + 3 \times y = 6x + 3 + 3y = 6x + 3y + 3
\]
**Equivalent**

---

**Option C: \((9-3)x+(4-0)y+3\)**
\[
(9-3)x + (4-0)y + 3 = 6x + 4y + 3
\]
This groups to:
\[
6x + 4y + 3
\]
**NOT Equivalent** (the \(y\) coefficient is \(4\), not \(3\))

---

**Option D: \((13-10)+(9x-3x)+(4y-y)\)**
\[
(13-10) + (9x-3x) + (4y-y) = 3 + 6x + 3y
\]
This simplifies to:
\[
6x + 3y + 3
\]
**Equivalent**

---

Based on this evaluation, the answer is indeed that option C is NOT equivalent.

So, yes, your original statement about the choice being C is correct. Thank you for your patience! The correct answer remains:

\[
\boxed{C}
\]