How do you solve #(x+2)/7 - (x-4)/8 = 3#?

1 Answer
seph
Jun 4, 2016

#x = 124#

Explanation:

#(x + 2)/7 - (x - 4)/8 = 3#

First, get rid of the denominators.
Do this by multiplying the equation with something that is a multiple of both denominators. The product of the denominators is one example. If you can find the LCM of the denominators pretty easily, do so to avoid needing to deal with larger values.

In the case of the given, the LCM is the product of the denominators, so we have no other choice here.

#56((x + 2)/7 - (x - 4)/8 = 3)#

Make sure to also scale the other side of the equation. We need to make sure that the equation still holds

#=> 8(x + 2) - 7(x - 4) = 56(3)#

#=> 8x + 16 - 7x + 28 = 168#

#=> x + 44 = 168#

#=> x = 124#

#=> x = 124#

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