Question

Solve the equation and also check your results:

x – (x-1)/2 = 1 – (x-2)/3

Answer 1

x – (x-1)/2 = 1 – (x-2)/3

Let us rearrange the equation

x – (x-1)/2 + (x-2)/3 = 1

By taking LCM for 2 and 3 which is 6

(6x – (x-1)3 + (x-2)2)/6 = 1

(6x – 3x + 3 + 2x – 4)/6 = 1

(5x – 1)/6 = 1

By cross-multiplying

5x – 1 = 6

5x = 6 + 1

x = 7/5

Let us verify the given equation now,

x – (x-1)/2 = 1 – (x-2)/3

By substituting the value of ‘x’ we get,

7/5 – (7/5 – 1)/2 = 1 – (7/5 – 2)/3

7/5 – (2/5)/2 = 1 – (-3/5)/3

7/5 – 2/10 = 1 + 3/15

(14 – 2)/10 = (15+3)/15

12/10 = 18/15

6/5 = 6/5

Hence, the given equation is verified.