Solve 3m+7/2=-2m+5/2 what is m

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