SOLUTION: Hello, my name is Eboni. Solving Equation. x-3/4x-4 +1/9= x-5/6x-6

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Question 792379: Hello, my name is Eboni.
Solving Equation.

x-3/4x-4 +1/9= x-5/6x-6
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
1/4x-4+1/9=1/6x-6
1/4x-1/6x=-6+4-1/9
3/12x-2/12x=-2 1/9
1/12x=-19/9
x=(-19/9)/(1/12)
x=-19/9*12/1
x=-228/9
x=-25 1/3

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hello, my name is Eboni.
Solving Equation.

x-3/4x-4 +1/9= x-5/6x-6

It it's %28x+-+3%29%2F%284x+-+4%29+%2B+1%2F9+=+%28x+-+5%29%2F%286x+-+6%29, then read on.

Note that x+%3C%3E+1

Denominators (4x - 4) and (6x - 6) factor to 4(x - 1) and 6(x - 1), respectively. Along with 9, we have denominators, 4(6)(9)(x - 1), which makes the LCD: 36(x - 1)

Therefore, %28x+-+3%29%2F%284x+-+4%29+%2B+1%2F9+=+%28x+-+5%29%2F%286x+-+6%29 becomes:

9(x - 3) + 4(x - 1) = 6(x - 5)

9x - 27 + 4x - 4 = 6x - 30

9x + 4x - 27 - 4 = 6x - 30

13x - 31 = 6x - 30

13x - 6x = - 30 + 31

7x = 1

highlight_green%28x+=+1%2F7%29

You can do the check!!

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