SOLUTION: How can you solve 3/4x-2/3=1/6x

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Question 1094212: How can you solve 3/4x-2/3=1/6x
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Make the equation unambiguous using parentheses for clarity.
What you show seems like it might be %283%2F4%29%2Ax-2%2F3=%281%2F6%29%2Ax.
but might be 3%2F%284x%29-2%2F3=1%2F%286x%29.

Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
.
How can you solve 3/4x-2/3=1/6x
~~~~~~~~~~~~~~~ 

Step 1.  Multiply both sides by 12, which is the common denominator.
         You will get an equivalent equation

         3*3x - 2*4 = 2x.   (1)



Step 2.  Collect the terms with "x" on the left side, while the constant terms on the right side.  Then combine like terms.


         When you move terms from one side of the equation to another side, do not forget to change their sign to the opposite one.


         So, continuing from the equation (1), the chain of operations can be like this:

         9x - 2x = 8  ====>  7x = 8  ====>  x = 8%2F7.


It is your solution and your answer.


Check.  The left side of the original equation is  %283%2F4%29%2A%288%2F7%29+-+2%2F3 = 24%2F28-2%2F3 = 72%2F84-56%2F84 = 16%2F84 = 4%2F21.

        The right side is %281%2F6%29%2A%288%2F7%29 = 4%2F21 - the same number.

        Hence, the solution is correct !