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August 24th, 2015, 06:29 PM   #1
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Math Homework

can someone help me do this problem for my sons homework. 1/3(2x-1) = 1/2(3x+1)
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August 24th, 2015, 07:19 PM   #2
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1/3(2x - 1) = 1/2(3x + 1)

Multiply both sides by the least common multiple of 2 and 3, which is 6:

2(2x - 1) = 3(3x + 1)

Expand:

4x - 2 = 9x + 3

Subtract 4x from each side:

-2 = 5x + 3

Subtract 3 from each side:

-5 = 5x

Solve for x:

x = -5/5 = -1
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August 25th, 2015, 05:02 AM   #3
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Did you mean $\displaystyle \frac{1}{3}(2x- 1)= \frac{1}{2}(3x- 1)$, which is what greg1313 assumed, or did you mean $\displaystyle \frac{1}{3(2x- 1)}= \frac{1}{2(3x- 1)}$, which is what I might have been inclined to think.

For both you start by "getting rid of the denominators". In the first you multiply both sides by (3)(2)= 6. For the second, multiply by 6(2x- 1)(3x- 1).
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August 25th, 2015, 05:06 AM   #4
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$\displaystyle \frac{1}{3(2x- 1)} = \frac{1}{2(3x- 1)}$ has no solutions.
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August 25th, 2015, 05:21 AM   #5
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It is not necessary that you multiply both sides by the least common multiple of the denominators. Any common multiple will do. The simplest way to do it is to multiply twice, once by each of the denominators (or, equivalently, multiply once by the product of the denominators). The drawback of this is that you then have more cancelling to do, and the cancelling can be non-trivial if you have multiplied by non-constant factors such as (x-2).
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August 26th, 2015, 03:32 AM   #6
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It's not absolutely necessary, but it will make things easier, especially if the LCM is easily found (as is the case here). Ideally, I should have included a note saying so; point well taken.

Last edited by greg1313; August 26th, 2015 at 03:52 AM.
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August 26th, 2015, 06:41 AM   #7
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After you have done all that, you will find that, as skipjack said, there are no solutions. Eventually, all "x" terms cancel, leaving "-2= -3" which is NOT true, for any value of x.
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August 26th, 2015, 10:48 AM   #8
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I was not assuming that interpretation of the question.

Last edited by greg1313; August 26th, 2015 at 10:54 AM.
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