SOLUTION: y = (a - x) / (2a - x) Solve for x in terms of y and a. Not sure how to solve.

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Question 1174949: y = (a - x) / (2a - x)
Solve for x in terms of y and a.
Not sure how to solve.

Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

"Solve for x in terms of y and a" means that your teacher wants you to get x all by itself, and have some expression with y's and/or a's on the other side.

Currently we have x on the right side and it's buried in a somewhat complicated fraction.

What we can do is multiply both sides by (2a-x) to move that term over. Then we apply distribution.

y = (a-x)/(2a-x)
y(2a-x) = a-x
y*2a+y(-x) = a-x
2ay - xy = a-x

After doing those steps, let's get all of the terms that have 'x' in them to one side. Everything else gets to the other side.

2ay - xy = a-x
2ay - xy+x = a-x+x
2ay - xy+x = a
2ay - xy+x-2ay = a-2ay
-xy+x = a-2ay
x-xy = a-2ay

Note how we can factor out x from the left side. We're using the distributive property. After factoring, divide both sides by (1-y) to fully isolate x

x-xy = a-2ay
x(1-y) = a-2ay
x = (a-2ay)/(1-y)

We've reached our goal of getting x all by itself on one side. The other side consists of some combination of 'a's and 'y's in which we are applying arithmetic operations to them.

Answer by MathTherapy(10557) (Show Source):
You can put this solution on YOUR website!

y = (a - x) / (2a - x)
Solve for x in terms of y and a.
Not sure how to solve.

y(2a - x) = a - x ------ Cross-multiplying
2ay - xy = a - x
- xy + x = a - 2ay
x(- y + 1) = a - 2ay