SOLUTION: 1/3x - 4=2x -1/7x

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Question 647938: 1/3x - 4=2x -1/7x
Answer by Algebraic(50) About Me  (Show Source):
You can put this solution on YOUR website!
Original equation: %28x%2F3%29+-+4+=+2x+-+%28x%2F7%29
Step 1: Put all of the factors under '1',and find an LCD
%28x%2F3%29+-+%284%2F1%29+=+%282x%2F1%29+-+%28x%2F7%29
We're going to need to find a common LCD (least common denominator) in order to be able to subtract the fractions. The number that both factors go into is '7', so multiply '7' to the numerator and denominator of %282x%2F1%29
%28x%2F3%29+-+%284%2F1%29+=+%282x%2F1%29%287%2F7%29+-+%28x%2F7%29
You'll get: %28x%2F3%29+-+%284%2F1%29+=+%2814x%2F7%29+-+%28x%2F7%29
Step 2: Combine like terms on the right side of the equation
%28x%2F3%29+-+%284%2F1%29+=+%2813x%2F7%29
Step 3: Subtract %28x%2F3%29 to both sides in order to avoid having to deal with negatives
%28x%2F3%29+-+%284%2F1%29+=+%2813x%2F7%29
-%284%2F1%29+=+%2813x%2F7%29-%28x%2F3%29
Step 4: Find a new LCD... in this case it is %287%29%283%29, so the new LCD is 21 Multiply both the numerator and denominator of both equations by factors that will make them equal 21
-%284%2F1%29+=+%2813x%2F7%29%283%2F3%29-%28x%2F3%29%287%2F7%29
Step 5: Simplify
-%284%2F1%29+=+%2813x%2F7%29%283%2F3%29-%28x%2F3%29%287%2F7%29
-%284%2F1%29+=+%2839x%2F21%29-%287x%2F21%29
-%284%2F1%29+=+%2832x%2F21%29
Step 6: Multiply the %2832x%2F21%29 by its inverse(opposite) in order to cancel it out and get the 'x' by itself
-%284%2F1%29+=+%2832x%2F21%29
-%284%2F1%29%2821%2F32%29+=+%2832x%2F21%29%2821%2F32%29
%28-84%2F32%29+=+x
Step 7: Simplify
%28-84%2F32%29+=+x
%28-21%2F8%29+=+x
The answer is %28-21%2F8%29+=+x or x+=+%28-21%2F8%29