Solve 1/2(4x + 6) = 1/3(9x - 24) with and without using the lcd of the fraction. are your answers the same?

For the answer to the question above asking to solve 1/2(4x + 6) = 1/3(9x - 24) with and without using the LCD of the fraction.
The problem is simple.

just multiply 1/2 to 4x + 6 which will result to 2x+3

same method on the 1/3 to 9x - 24 and it will result to 3x-8

2x+3 = 3x - 8

3x-2x = 8+3

then the answer will be  x= 11

Best answer that i found on yahoo ok   set :   x= length of 2nd piece in cm  x- 3= length of 1st piece in cm  x-4= length of 3rd piece in cm  then since you know they all came from the 20 cm ribbon you add them together and set them equal to 20x+ x-3 +x-4 = 20  3x - 7= 20  3x= 27  x= 9  the shortest piece is the third piece which is x- 4  x-4  9-4 = 5  the length of the smallest piece is 5 cm.  the other lengths are  9 cm  6 cm