Question

Which of the following expressions is not equivalent to -12x+36?

A. -3x+20-9x+16
B. 4(-3x+9)
C. 20x-2(4x-18)
D. -6x+2(-3x+6)+24

Answer 1

Option C

20x - 2(4x - 18) is not equivalent to given expression -12x + 36

Solution:

Given expression is:

-12x + 36

We have to find out the expressions that are not equivalent

Let us check the options one by one

Option A

`-3x+20-9x+16`

Combine the like terms

`-3x -9x + 20 + 16`

Add the like terms and add the constants

`-12x + 36`

Thus this expression is equivalent to given expression

Option B

`4(-3x + 9)`

By distributive property we can say,

a(b + c) = ab + bc

`4(-3x + 9) = (4 * -3x) + (4 * 9)\\\\4(-3x + 9) =-12x + 36`

Thus this expression is equivalent to given expression

Option C

`20x - 2(4x - 18)`

Similarly, using distributive property,

`20x - 2(4x - 18) = 20x -8x + 36 = 12x +36\\\\20x - 2(4x - 18) = 12x + 36`

But 12x + 36 is not equivalent to given expression -12x + 36

Option D

`-6x+2(-3x+6)+24`

Similarly, using distributive property,

`-6x+2(-3x+6)+24 = -6x -6x + 12 + 24 = -12x + 36`

Thus this expression is equivalent to given expression