Solve for x: 2 (x+1/3) = 4 (x-1) Put each term in x+1/3 over the common denominator 3: x+1/3 = (3 x)/3+1/3: 2 (3 x)/3+1/3 = 4 (x-1) (3 x)/3+1/3 = (3 x+1)/3: 2 (3 x+1)/3 = 4 (x-1) Multiply both sides by 3: (3×2 (3 x+1))/3 = 3×4 (x-1) (3×2 (3 x+1))/3 = 3/3×2 (3 x+1) = 2 (3 x+1): 2 (3 x+1) = 3×4 (x-1) 3×4 = 12: 2 (3 x+1) = 12 (x-1) Expand out terms of the left hand side: 6 x+2 = 12 (x-1) Expand out terms of the right hand side: 6 x+2 = 12 x-12 Subtract 12 x from both sides: (6 x-12 x)+2 = (12 x-12 x)-12 6 x-12 x = -6 x: -6 x+2 = (12 x-12 x)-12 12 x-12 x = 0: 2-6 x = -12 Subtract 2 from both sides: (2-2)-6 x = -12-2 2-2 = 0: -6 x = -12-2 -12-2 = -14: -6 x = -14 Divide both sides of -6 x = -14 by -6: (-6 x)/(-6) = (-14)/(-6) (-6)/(-6) = 1: x = (-14)/(-6) The gcd of -14 and -6 is -2, so (-14)/(-6) = (-2×7)/(-2×3) = (-2)/(-2)×7/3 = 7/3: Answer: | | x = 7/3
