SOLUTION: Hello: I am asked to solve for x x - z = xy + w This is a practice exam so I am given the answer of: w + z ----- 1 - y I do not understand how they arrived at this

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Question 44888: Hello:
I am asked to solve for x
x - z = xy + w
This is a practice exam so I am given the answer of:
w + z
-----
1 - y
I do not understand how they arrived at this answer. To be honest I do not understand how to approach this problem. I can make it this far:
x - z = xy + w
x = xy + w + z
x - xy = w + z
Thank you very much for your time and help.
David
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You were 1 step away.
x+-+z+=+xy+%2B+w
x+=+xy+%2B+w+%2B+z
x+-+xy+=+w+%2B+z
You added z to both sides, then you subtracted
xy from both sides. Fine so far.
Now what to do with the
x - xy
Substitute numbers for the letters
x+=+5
y+=+7
5+-+5%2A7
or, 5 - 35 = -30
You should get the same answer if you factor out the 5
5%281+-+7%29
5%2A%28-6%29+=+-30
This is called the distributive law of algebra.
Back to the equation
x+-+xy+=+w+%2B+z
x%281+-+y%29+=+w+%2B+z
divide both sides by (1 - y)
x+=+%28w+%2B+z%29+%2F+%281+-+y%29 answer

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x - z = xy + w
You need to get the x's on one side of the equal sign.
So, subtract xy from both sides to get:
x-xy-z=w
Get rid of the terms that have no x and are on the same side as the x terms.
Add z to both sides to get:
x-xy=w+z
Now, factor out the x to get:
x(1-y)=w+z
Divide both sides by (1-y) to get:
x=(w+z)/(1-y)
Cheers,
Stan H.