Question

Are (2x+4)/(3x+6) and 2/3 equivalent expressions? Please explain why or why not.

Answer 1

(2x + 4)/(3x + 6) = 2/3 (cross multiply)
(3)(2x+ 4) = (2)(3x + 6)
6x + 12 = 6x + 12
They are equivalent expressions because they equal each other.

Answer 2

By the way, the x has infinite solutions....it can be anything, and it will still equal.

Answer 3

Another way to solve is:

\[(2x + 4 ) = 2 ( x+2)\]
\[(3x + 6) = 3(x + 2)\]
Now \[\frac{ 2 (x + 2) }{ 3 (x + 2) } = \frac{ 2 }{3 }\]
Since (x+2) cancels out in both numerator and denominator

Answer 4

@rajee_sam ....I believe your way is easier :)