SOLUTION: 2/3y+4=2x rewrite the function that y is a function of x

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Question 223382: 2/3y+4=2x
rewrite the function that y is a function of x
Found 2 solutions by checkley77, jsmallt9:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
2/3y+4=2x
2Y/3+4=2X
X=(2Y/3+4)/2
X=(2Y/3)*1/2+4/2
X=2Y/6+2
X=Y/3+2 ANS.

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure if the equation is %282%2F3%29y%2B4+=+2x or 2%2F%283y%29+%2B+4+=+2x. I'll do both and you pick the right one.

When writing "y as a function of x" it means solve the equaiton for y and this is what I shall do:
  • %282%2F3%29y%2B4+=+2x
    1. Subtract 4 from each side:
      %282%2F3%29y+=+2x+-+4
    2. Multiply both sides by the reciprocal of 2/3 (which is 3/2):
      %283%2F2%29%282%2F3%29y+=+%283%2F2%29%282x-4%29
      y+=+3x+-+6
      This equation expresses y as a function of x.
  • 2%2F%283y%29+%2B+4+=+2x
    1. Multiply both sides by 3y:
      %283y%29%282%2F%283y%29+%2B+4%29+=+%283y%29%282x%29.
      2+%2B+12y+=+6xy
    2. Subtract 12y from each side (to get the y terms together):
      2+=+6xy+-+12y
    3. Factor out y on the right side:
      2+=+y%286x+-+2%29
    4. Divide both sides by (6x-2):
      2%2F%286x-2%29+=+%28y%286x-2%29%29%2F%286x-2%29
      The (6x-2)'s cancel on the right:
      2%2F%286x-2%29+=+y
      This equation expresses y as a function of x.

(Note: a solution provided by another expresses x as a function of y which is not what the problem asks for.)