SOLUTION: Please help me solve this equation: 1/6(3y-2)=1 -1/3(y-1) This is what I have come up with: 1/2y -1/3 = 1 -1/3+1/3, then I multiplied both sides by GCF of 6 to give me: 3y -

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this equation: 1/6(3y-2)=1 -1/3(y-1) This is what I have come up with: 1/2y -1/3 = 1 -1/3+1/3, then I multiplied both sides by GCF of 6 to give me: 3y -      Log On


   

Question 177273: Please help me solve this equation:
1/6(3y-2)=1 -1/3(y-1)
This is what I have come up with:
1/2y -1/3 = 1 -1/3+1/3, then I multiplied both sides by GCF of 6 to give me:
3y -2 = 6 -2y+2, then combine like terms
3y -2 = 4 -2y,
5y = 6
y = 6/5
When I try and plug in my answer it doesn't check:
1/6(18/5 -2) = 1 -1/3(6/5 -1), multiply by GCF of 15,
15(3/5 -1/3) = (1 -6/15 + 1/3)15
9 -5 = 15 -6 +5 Does not check
Thank you,
Betty
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F6%29%283y-2%29=1+-%281%2F3%29%28y-1%29 Start with the given equation.


3y-2=6+-2%28y-1%29 Multiply EVERY term (that's not in a set of parenthesis) by the LCD 6 to clear the fractions.


3y-2=6-2y%2B2 Distribute.


3y-2=-2y%2B8 Combine like terms on the right side.


3y=-2y%2B8%2B2 Add 2 to both sides.


3y%2B2y=8%2B2 Add 2y to both sides.


5y=8%2B2 Combine like terms on the left side.


5y=10 Combine like terms on the right side.


y=%2810%29%2F%285%29 Divide both sides by 5 to isolate y.


y=2 Reduce.


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Answer:

So the answer is y=2




Check:


%281%2F6%29%283y-2%29=1+-%281%2F3%29%28y-1%29 Start with the given equation.


%281%2F6%29%283%282%29-2%29=1+-%281%2F3%29%282-1%29 Plug in y=2


%281%2F6%29%286-2%29=1+-%281%2F3%29%282-1%29 Multiply


%281%2F6%29%284%29=1+-%281%2F3%29%281%29 Subtract


4%2F6=1+-1%2F3 Multiply


2%2F3=1+-1%2F3 Reduce


2%2F3=2%2F3 Combine like terms. So this verifies our answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1/6)(3y-2) = 1 - (1/3)(y-1)
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Multiply thru by 6 to get:
(3y-2) = 6 - 2(y-1)
3y-2 = 6 - 2y + 2
5y = 10
y = 2
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Cheers,
Stan H.