Question

I would love a step by step explanation on how to do this problem.
(5-x)/(x) + 3/4 = 7/x

So far I have done this:
Since 4x goes into all of the denominators, I am multiply all numerators by it, so that we can cancel out the denominators.
(4x)(5-x)/(x) + (4x)(3)/x = (4x)(7)/x

Here is where the trouble comes in. I was wondering, because of the distributive property, do I multiply the (4x)(5-x) like so: 20x-4x² ? Thank you in advance!

Answer 1

multiply it all by x to get rid of denoms

Answer 2

then gather like terms

Answer 3

divide off the x constant

Answer 4

You can, but that's the long way around. Use the commutative property to split up the 4x. The four distributes across the binomial, the x cancels with the denominator.

Answer 5

5-x/x + 3/4 = 7/x

5-x + 3/4 x = 7

-x + 3/4 x = 7-5

x(-1+ 3/4) = 7-5

x = (7-5)/(-1+ 3/4)

Answer 6

\[(4x)(5-x)/(x) + (4x)(3)/x = (4x)(7)/x\]\[(20-4x) + 12 = 28\]\[4x=4\]\[x=1\]

Answer 7

really? I get x = -8 hmmm

Answer 8

In my book -8 is the correct answer.

Answer 9

tada!! lol

Answer 10

personally I woulda just set it equal to -8 to begin with and work my way backwards to an x -8=x :)

Answer 11

That might be a good idea. :P Thank you both for the help!

Answer 12

I found my mistake. The problem reflects a denominator of 4 in the second term. I copied his intermediate work, which slipped an x in its place. Poor attention to detail here; sorry.

Answer 13

no soup for you!!