How do you solve #5/(2x+7) = -9/(4x+14)#?

1 Answer
Sep 27, 2015

Answer:

This equality has no solutions.

Explanation:

An identity holds if and only if the identity between the inverses hold (as long as you don't have something like #0=0# of course). So, in you case, you have that

#5/{2x+7} = - 9/{4x+14} \iff {2x+7} /5 = {4x+14}/9#

The only thing we have to take care about is to make sure that the original denominators aren't zero, i.e. #2x+7 \ne 0# and #4x+14 \ne 0#, both satisfied by #x \ne -7/2#.

Now we can go on searching for the solutions:

#{2x+7} /5 = {4x+14}/9 \iff 9(2x+7) = 5(4x+14)#

by cross-multiplication, and expanding we get

#18x+63=20x+70#. Isolating the #x#-terms and the costants, we finally get

#-2x=7#, and finally solve for #x=-7/2#

This is the value we couldn't consider, so the equality has no solutions.