Solve for x: 1/2+(6 x+5)/3 = 1/6 Put each term in 1/2+(6 x+5)/3 over the common denominator 6: 1/2+(6 x+5)/3 = 3/6+(2 (6 x+5))/6: 3/6+(2 (6 x+5))/6 = 1/6 3/6+(2 (6 x+5))/6 = (3+2 (6 x+5))/6: (3+2 (6 x+5))/6 = 1/6 2 (6 x+5) = 12 x+10: (12 x+10+3)/6 = 1/6 Add like terms. 3+10 = 13: (12 x+13)/6 = 1/6 Multiply both sides of (12 x+13)/6 = 1/6 by 6: (12 x+13)/(6/6) = (1/6)/(1/6) 1/(6/6) = 1: 12 x+13 = (1/6)/(1/6) (1/6)/(1/6) = 1: 12 x+13 = 1 Subtract 13 from both sides: 12 x+(13-13) = 1-13 13-13 = 0: 12 x = 1-13 1-13 = -12: 12 x = -12 Divide both sides of 12 x = -12 by 12: (12 x)/12 = (-12)/12 12/12 = 1: x = (-12)/12 The gcd of -12 and 12 is 12, so (-12)/12 = (12 (-1))/(12×1) = 12/12×-1 = -1: Answer: | | x = -1
