# solving equation

Hello,

I have a problem with solving this equation i know the answer it shoud be -6 but i can't get it right could anyone please help me ?

2.(x/3 + 1) = x/4 - 1/2
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Commented:
2/3x+2=x/4-1/2
multiply by 12
8x+24=3x-6
5x=-30
x=-6

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Commented:
Just to clarify: By "2/3x" here I mean "2/3*x" or "2x/3".
\Commented:
There is often no one path to the final destination. Here's another path:

2.(x/3 + 1) = x/4 - 1/2

Divide by 2 to both sides to simplify left hand side:
(x/3 + 1) = x/8 - 1/4

Remove parens:
x/3 + 1 = x/8 - 1/4

Subtract 1 to both sides:
x/3  = x/8 - 1/4 - 1

Subtract x/8 to both sides:
x/3 - x/8 =  - 1/4 - 1

Multiply by 24 on both sides to remove denominators on left hand side (Note: chose 24, since 24 = 3*8)
8x - 3x =  24*(-5/4)
5x = 6*(-5)
5x = -30

Divide by 5 on both sides:
x = -6

Commented:
Here it is using the lowest common demoninator of 12

Original equation
2 (x/3 + 1) = x/4 - 1/2

Divide by lowest common denominator
2(4x/12 + 12/12) = 3x/12 - 6/12

Remove parents by multiplying through the 2 on the left side
8x/12 + 24/12 = 3x/12 - 6/12

Subtract 3x/12  and -24/12
8x/12 - 3x/12 = -6/12 - 24/12

Results of the above calculation
5x/12 = -30/12

Multiply both sides by 12 to remove the denominator
5x=-30

Divide both sides by 5 to get x
x=-6
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