SOLUTION: x/3=x+10/6 I can not figure this one out!!! Can anyone please help me???

Question 247180: x/3=x+10/6

I can not figure this one out!!! Can anyone please help me???
Found 2 solutions by College Student, Theo:
Answer by College Student(505) (Show Source): You can put this solution on YOUR website!
Hello.

Is it ...or... ???

When using our website, please use parenthesis to distinguish the numerators and denominators from neighboring integers. For the time being, I'm going to presume it's the second one.

If we multiply by six on both sides of the equation, we can get rid of both denominators.

Now, let's solve for x:

Please repost if I misinterpreted the original problem.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x/3=x+10/6

is this (x/3) = (x+10)/6

or is this (x/3) = x + (10/6)

If I follow the rules of algebra, without parentheses, it would be the second form.

assuming it is the first form, then your equation is:

(x/3) = (x+10)/6

multiply both sides of this equation by 6 to get:

6 * (x/3) = 6 * (x+10) / 6 which becomes:

2 * x = x + 10

subtract x from both sides of this equation to get x = 10

substitute in original equation to get:

10/3 = 20/6 which is true so the answer of x = 10 is good.

assuming it is the second form, then your equation is:

(x/3) = x + (10/6)

multiply both sides of this equation by 6 to get:

6 * (x/3) = 6 * (x + 10/6) which becomes:

2 * x = 6 * x + 10

subtract 6 * x from both sides of this equation to get:

2 * x - (6 * x) = 10

combine like terms to get:

-4 * x = 10

divide both sides by (-4) to get:

x = -10/4

substitute in original equation to get:

((-10/4)/3)) = (-10/4) + (10/6)

multiply both sides of this equation by 6 to get:

6 * ((-10/4)/3) = 6 * ((-10/4) + (10/6))

simplify to get:

(-20/4) = (-60/4) + (60/6)

simplify further to get:

-5 = -15 + 10

combine like terms to get:

-5 = -5 confirming that the answer of x = -10/4 is good.

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