Solve for m:3 m + 7/2 = 5/2 - 2 m Put each term in 3 m + 7/2 over the common denominator 2: 3 m + 7/2 = (6 m)/2 + 7/2:(6 m)/2 + 7/2 = 5/2 - 2 m (6 m)/2 + 7/2 = (6 m + 7)/2:(6 m + 7)/2 = 5/2 - 2 m Put each term in 5/2 - 2 m over the common denominator 2: 5/2 - 2 m = 5/2 - (4 m)/2:(6 m + 7)/2 = 5/2 - (4 m)/2 5/2 - (4 m)/2 = (5 - 4 m)/2:(6 m + 7)/2 = (5 - 4 m)/2 Multiply both sides by 2:6 m + 7 = 5 - 4 m Add 4 m to both sides:6 m + 4 m + 7 = (4 m - 4 m) + 5 4 m - 4 m = 0:6 m + 4 m + 7 = 5 6 m + 4 m = 10 m:10 m + 7 = 5 Subtract 7 from both sides:10 m + (7 - 7) = 5 - 7 7 - 7 = 0:10 m = 5 - 7 5 - 7 = -2:10 m = -2 Divide both sides of 10 m = -2 by 10:(10 m)/10 = (-2)/10 10/10 = 1:m = (-2)/10 The gcd of -2 and 10 is 2, so (-2)/10 = (2 (-1))/(2×5) = 2/2×(-1)/5 = (-1)/5:Answer: m = (-1)/5
