Gloria says the two expressions 1/4 (12x + 24) - 9x and - 6 (x + 1) are equivalent. Is she correct? Explain why or why not.

So first distribute

1/4 (12x+24) = 3x+8

so 3x+8-9x=8-6x

-6 (x+1) = - 6x-6

8-6x is not equal to - 6-6x

so she is NOT correct, they are not equivilent

The first expression is equal to 3x + 24 - 9x, or 24 - 6x, and the second equation equals 6-6x. If you set them equal to eachother, you get 24 - 6x = 6 - 6x. The 6x's cancel out, so you're left with 24 = 6, which is not true. The expressions are not equivalent.