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

Question

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 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 2

is that correct

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

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

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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 \(3\))

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

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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:

\[ \boxed{C} \]