Given m – (m – 1)/2 = 1 – (m – 2)/3
(2m – m + 1)/2 = (3 – m + 2)/3
(m + 1)/2 = (5 – m)/3
(m + 1)/2 = (5/3) – (m/3)
(m/2) + (1/2) = (5/3) – (m/3)
Transposing (m/3) to LHS and (1/2) to RHS
(m/2) + (m/3) = (5/3) – (1/2)
(3m + 2m)/6 = (10 – 3)/6
5m/6 = (7/6)
5m = 7
Dividing both sides by 5, we get
5m/5 = 7/5
m = 7/5
Verification:
Substituting m = 7/5 on both sides, we get
(7/5) – (7 – 5)/10 = 1 – (7 – 10)/15
(7/5) – (2/10) = (15 + 3)/15
(14 – 2)/10 = (15 + 3)/15
12/10 = 18/15
(6/5) = (6/5)
Thus LHS = RHS
Hence, verified.