SOLUTION: I hate fractions. I think I understand absolute value enough but when you throw fractions into the mix I get confused. This problem also has 2 fractions so im real confused.
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Question 179445: I hate fractions. I think I understand absolute value enough but when you throw fractions into the mix I get confused. This problem also has 2 fractions so im real confused.
this is the problem |x-1/3|=|1/2x+1/6|
x-1/3=1/2x+1/6
First I subtract 1/3 from each side to get
x=1/2x+1/9
then I subtract the 1/2x from both sides to get
1/2x=1/9
this is where i get confused. if i divide by the 1/2 i get 2/9. but my books says the answer is 1 ----so where did i go wrong. I know there is another side to the problem still,but if I cant get the first half then?????? Answer by MissionPossible(18) (Show Source):
You can put this solution on YOUR website! You made the mistake.
this is the problem |x-1/3|=|1/2x+1/6|
x-1/3=1/2x+1/6 ------>This is wrong.
You can not just pull it out from the absolute
The theory is If |A|=|B| Then ---> A^2 = B^2
|x-1/3|=|1/2x+1/6| -----> (x-1/3)^2 = (1/2x+1/6)^2
(x-1/3)^2 = (1/2x+1/6)^2
x^2 -(2/3)x + (1/9) = (1/4)x^2 +(1/6)x + (1/36)-------(1)
36 * Eq(1)
36x^2 - 24x + 4 = 9x^2 + 6x + 1
27x^2 - 30x + 3 = 0
divide by 3
9x^2 - 10x + 1 = 0
(9x -1 )(x-1) = 0
Then x = 1/9 , 1 Ans.
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