I can not get the correct answer for y

Question

     3        -   6y      =7   

   y-2           2-y

 

I tried adding (y-2) and (2-y) to both sides, but I got the answer y= 2 and I know that is wrong.

 

 

this problem does not come out the way I typed it.

 

 This problem is actually in division form

y-2 ÷ 3 - 2-y ÷ 6y =7

 

 

Answer 1

Multiply both sides of the equation by the LCD.  LCD is (y - 2)(2 - y).

 

You get the resulting equation

 

3(2 - y) - 6y(y - 2) = 7(y - 2)(2 - y)

 

6 - 3y - 6y² + 12y = 7(2y - y² - 4 + 2y)

 

6 + 9y - 6y² = 28y - 7y² - 28

 

 

Move all terms to the left side of equation.

 

y² - 19y + 34 = 0

 

 

Solve for x from this quadratic equation.

 

(y - 17)(y - 2) = 0

 

 

Setting the factors equal to zero, you get

 

y = 2       and       y = 17

 

 

Now just validate them by plugging them into the original equation.

Answer 2

You cannot add different amounts to both sides....

 

3 - 6y = 7

 

-6y = 7 - 3   <-- subtracts 3 from both sides

 

-6y = 4

 

y = -4/6   <--- divides both sides by -6

y = -2/3  <-- reduce to lowest terms

 

check :   3 - 6(-2/3) = 3 -  6/1*-2/3 = 3 -  (-12/3) = 3 - (-4) = 7