Solve for x:(5 (x - 1/3))/(8) = 5/12 Put each term in x - 1/3 over the common denominator 3: x - 1/3 = (3 x)/3 - 1/3:(5 (3 x)/3 - 1/3)/(8) = 5/12 (3 x)/3 - 1/3 = (3 x - 1)/3:(5 (3 x - 1)/3)/(8) = 5/12 3×8 = 24:(5 (3 x - 1))/24 = 5/12 Multiply both sides of (5 (3 x - 1))/24 = 5/12 by 24/5:(24×5 (3 x - 1))/(5×24) = (24×5)/(5×12) (24×5)/(5×12) = (24×5)/(5×12):(24×5 (3 x - 1))/(5×24) = (24×5)/(5×12) (24×5 (3 x - 1))/(5×24) = (5×24)/(5×24)×(3 x - 1) = 3 x - 1:3 x - 1 = (24×5)/(5×12) (24×5)/(5×12) = 5/5×24/12 = 24/12:3 x - 1 = 24/12 The gcd of 24 and 12 is 12, so 24/12 = (12×2)/(12×1) = 12/12×2 = 2:3 x - 1 = 2 Add 1 to both sides:3 x + (1 - 1) = 1 + 2 1 - 1 = 0:3 x = 2 + 1 2 + 1 = 3:3 x = 3 Divide both sides of 3 x = 3 by 3:(3 x)/3 = 3/3 3/3 = 1:x = 3/3 3/3 = 1:Answer: x = 1
