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
The expression that is NOT equivalent to 9x+4y+13-3x-y-10 is:
D. (13-10)+(9x-3x)+(4y-y)
To find the expression that is NOT equivalent to 9x+4y+13-3x-y-10, we need to simplify each of the options and check if they are equivalent to the given expression.
A. 3(2x+y+1)
Distributing the 3: 3 * 2x + 3 * y + 3 * 1 = 6x + 3y + 3
B. 6x+3(1+y)
Distributing the 3: 6x + 3 * 1 + 3 * y = 6x + 3 + 3y = 6x + 3y + 3
C. (9-3)x+(4-0)y+3
Simplifying the terms in the parentheses: 6x + 4y + 3
D. (13-10)+(9x-3x)+(4y-y)
Simplifying the terms in the parentheses and combining like terms:
3 + 6x - 3x + 4y - y = 3x + 3y + 3
From the simplifications above, we can see that option D (3x + 3y + 3) is NOT equivalent to the given expression (9x+4y+13-3x-y-10).
Therefore, the answer is D. (3x + 3y + 3).
To determine which expression is NOT equivalent to 9x + 4y + 13 - 3x - y - 10, we need to simplify all the given options and compare them to the original expression.
Original expression: 9x + 4y + 13 - 3x - y - 10
Option A: 3(2x + y + 1)
To simplify option A, distribute the 3 to each term within the parentheses:
3 * 2x + 3 * y + 3 * 1 = 6x + 3y + 3
This expression is NOT equivalent to the original expression because it has an extra +3 at the end.
Option B: 6x + 3(1 + y)
To simplify option B, distribute the 3 to each term within the parentheses:
6x + 3 * 1 + 3 * y = 6x + 3 + 3y
This expression is NOT equivalent to the original expression because it has an extra +3 in the middle.
Option C: (9 - 3)x + (4 - 0)y + 3
To simplify option C, perform the operations within the parentheses and combine like terms:
(9 - 3)x + (4 - 0)y + 3 = 6x + 4y + 3
This expression is equivalent to the original expression.
Option D: (13 - 10) + (9x - 3x) + (4y - y)
To simplify option D, perform the operations within the parentheses and combine like terms:
(13 - 10) + (9x - 3x) + (4y - y) = 3 + 6x + 3y
This expression is NOT equivalent to the original expression because it has an extra +3 at the beginning.
Therefore, the expression that is NOT equivalent to 9x + 4y + 13 - 3x - y - 10 is Option B: 6x + 3(1 + y).