Find those x satisfying each of the equations below:

|x| = |x + 1|

This can be solved in the following cases:

Case1 : when x>-1, |x + 1| = x + 1 and x>0, |x| = x

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

Case2 : when x>-1, |x + 1| = x + 1 and x<0, |x| = -x

x + 1 = -x

⇒ 2x = -1

⇒ x = -1/2………………..eq(2)

Case3 : when x<-1, |x + 1| = -(x + 1) and x>0, |x| = x

-(x + 1) = x

⇒ -x-1 = x

⇒ -2x = 1

⇒ x = ………………..eq(3)

Case4 : when x<-1, |x + 1| = -(x + 1) and x<0, |x| = -x

-(x + 1) = -x

⇒ -x-1 = -x ⇒ 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.