SOLUTION: Please help me solve this equation: x+\frac{1}{2}=\frac{5}{3}-\frac{x}{6}

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Question 1206308: Please help me solve this equation: x+\frac{1}{2}=\frac{5}{3}-\frac{x}{6}
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

    x + 1%2F2 = 5%2F3 - x%2F6.


Multiply both sides (each term) by 6.  You will get

    6x + 3 = 10 - x


Collect the terms with x on the left side; the constant term on the right side.

When moving the terms from left to right and from right to left, change their sides to opposite

   6x + x = 10 - 3


Combine like terms

    7x = 7


Divide both sides by 7

    x = 1.


At this point, the solution is complete.


ANSWER.  x= 1.

Solved.

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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x%2B1%2F2=5%2F3-x%2F6
x%2Bx%2F6=5%2F3-1%2F2
6x%2F6%2Bx%2F6=%285%2A2%29%2F%283%2A2%29-%281%2A3%29%2F%282%2A3%29
7x%2F6=10%2F6-3%2F6
7x%2F6=7%2F6...if denominators same, numerators must be same too
7x=7
x=1