SOLUTION: What is the inverse of y=2x+1 my work: x=2y+1 I just want to make sure all I have to do is switch the x and y.

Algebra ->  Inverses -> SOLUTION: What is the inverse of y=2x+1 my work: x=2y+1 I just want to make sure all I have to do is switch the x and y.       Log On


   

Question 697281: What is the inverse of y=2x+1
my work:
x=2y+1
I just want to make sure all I have to do is switch the x and y.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You are doing OK.
Keep on going.
You have to solve for y.
You should end up with
y=%281%2F2%29x-1%2F2 (answer I would prefer)
y=%281%2F2%29%28x-1%29 and y=x%2F2-1%2F2 are alternative equivalent answers.

Here's how you would solve for y:
x=2y%2B1 --> x-1=2y%2B1-1 --> x-1=2y (subtracting 1 from both sides of the equal sign)
x-1=2y --> %28x-1%29%2F2=2y%2F2 --> %28x-1%29%2F2=y (dividing both sides by 2)
%28x-1%29%2F2=y is the same as y=%28x-1%29%2F2 because the equal sign works both ways,
and y=%28x-1%29%2F2 is the same as y=%281%2F2%29%28x-1%29 because dividing by 2 is the same as multiplying by 1/2.
y=%281%2F2%29%28x-1%29 --> y=%281%2F2%29x%2B%281%2F2%29%28-1%29 --> y=%281%2F2%29x-1%2F2 (applying the distributive property)
y=%281%2F2%29x-1%2F2 --> y=x%2F2-1%2F2 because dividing by 2 is the same as multiplying by 1/2, so that %281%2F2%29x=x%2F2.