The recommended approach for such equations is to eliminate fractions first, by multiplying by the LCM of the denominators. You can simply simplify, then work them as a 2-step linear equation, doing your arithmetic with the fractions as they are.
a) (5x-1)/7 + (4x-3)/2 -(3-2x)/2 = 6 . . . . . given
... 2(5x -1) +7(4x -3) -7(3 -2x) = 84 . . . . . multiply by 14
... 10x -2 +28x -21 -21 +14x = 84 . . . . . . eliminate parentheses
... 52x -44 = 84 . . . . . . . . . . . . . . . . . . . . collect terms
... 52x = 128 . . . . . . . . . . . . . . . . . . . . . . . add 44
... x = 32/13 . . . . . . . . . . . . . . . . . . . . . . . . divide by 52 and simplify
b) (4x−3)/2 − (5−2x)/3 − (3x−4)/3 = 5 . . . given
... 2x -3/2 -5/3 +(2/3)x -x +4/3 = 5 . . . . . . .eliminate parentheses
... (5/3)x -11/6 = 5 . . . . . . . . . . . . . . . . . . . . simplify
... (5/3)x = 41/6 . . . . . . . . . . . . . . . . . . . . . . add 11/6
... x = (41/6)/(5/3) = 41/10 . . . . . . . . . . . . . .divide by the coefficient of x
_____
Using the first method, you're dealing with integers and you can do a lot of the math in your head. Using the second method, you're dealing with fractions and mixed numbers. A calculator can be helpful, especially if it handles arithmetic with fractions nicely, as many graphing calculators do.
