SOLUTION: summer homework,forget how to do it- five x minus 1 over 9 plus two x plus 4 over 6 equals three x minus four over 3. Solve for x.thank you

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Question 95372: summer homework,forget how to do it- five x minus 1 over 9 plus two x plus 4 over 6 equals three x minus four over 3. Solve for x.thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
five x minus 1 over 9 plus two x plus 4 over 6 equals three x minus four over 3. Solve for x.
:
Assume you mean:
%28%285x-1%29%29%2F9 + %28%282x%2B4%29%29%2F6 = %28%283x-4%29%29%2F3
;
Choose a multiplier that is a multiple of all 3 denominators, 18 will work:
18%28%285x-1%29%29%2F9 + 18%28%282x%2B4%29%29%2F6 = 18%28%283x-4%29%29%2F3
:
Cancel out the denominators and you have:
2(5x-1) + 3(2x+4) = 6(3x-4)
:
Multiply what's inside the brackets:
10x - 2 + 6x + 12 = 18x - 24
:
16x + 10 = 18x - 24
:
16x - 18x = -24 - 10
:
-2x = -34
:
x = -34/-2
:
x = +17
:
:
Check our solution; substitute 17 for x in the original equation
%28%285%2817%29-1%29%29%2F9 + %28%282%2817%29%2B4%29%29%2F6 = %28%283%2817%29-4%29%29%2F3
:
%28%2885-1%29%29%2F9 + %28%2834%2B4%29%29%2F6 = %28%2851-4%29%29%2F3
:
%28%2884%29%29%2F9 + %28%2838%29%29%2F6 = %28%2847%29%29%2F3
:
Put over the common denominator of 18 and you have:
%28%28168%29%29%2F18 + %28%28114%29%29%2F18 = %28%28282%29%29%2F18; confirms our solution