Find those x satisfying each of the equations below:

|x – 3| = |x – 4|

This can be solved in the following cases:

Case1 : when x>3, |x-3| = x-3 and x>4, |x-4| = x-4

x-3 = x-4 ⇒ no solution as x gets cancelled out on both sides……….eq(1)

Case2 : when x>3, |x-3| = x-3 and x<4, |x-4| = -(x-4)

x-3 = -(x-4)

⇒ x-3 = 4-x

⇒ 2x = 4 + 3

⇒ 2x = 7

⇒ x = ………………..eq(2)

Case3 : when x<3, |x-3| = -(x-3) and x>4, |x- 4| = x-4

-(x-3) = (x-4)

⇒ -x + 3 = x-4

⇒ -2x = -4-3 = -7

⇒ 2x = 7

⇒ x = ………………..eq(3)

Case4 : when x<3, |x-3| = -(x-3) and x<4, |x-4| = -(x-4)

-(x- 3) = -(x-4)

⇒ -x + 3 = -x + 4 ⇒ no solution as x gets cancelled out on both sides…………………..eq(4)

Now from eq(2) ans eq(3), we have x = as the solution of the equation.