Solve the equation. Also, verify the result.m – (m – 1)/2 = 1 –

1.	Solve the equation. Also, verify the result.m – (m – 1)/2 = 1 – (m – 2)/3
Answer» 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.

Solve the equation. Also, verify the result.m – (m – 1)/2 = 1 – (m – 2)/3

Answer»

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.