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
[tex]-3x+20-9x+16[/tex]
Combine the like terms
[tex]-3x -9x + 20 + 16[/tex]
Add the like terms and add the constants
[tex]-12x + 36[/tex]
Thus this expression is equivalent to given expression
[tex]4(-3x + 9)[/tex]
By distributive property we can say,
a(b + c) = ab + bc
[tex]4(-3x + 9) = (4 \times -3x) + (4 \times 9)\\\\4(-3x + 9) =-12x + 36[/tex]
Thus this expression is equivalent to given expression
[tex]20x - 2(4x - 18)[/tex]
Similarly, using distributive property,
[tex]20x - 2(4x - 18) = 20x -8x + 36 = 12x +36\\\\20x - 2(4x - 18) = 12x + 36[/tex]
But 12x + 36 is not equivalent to given expression -12x + 36
[tex]-6x+2(-3x+6)+24[/tex]
Similarly, using distributive property,
[tex]-6x+2(-3x+6)+24 = -6x -6x + 12 + 24 = -12x + 36[/tex]
Thus this expression is equivalent to given expression
