The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is

Step-by-step solution

Critical points: x=-3 and x=1 . Case x x^2+4x+1=0 x=-2 3 . Only x=-2- 3 -3.73 lies in (- ,-3) . (1 solution) Case -3 x x^2+2x-1=0 x=-1 2 . Both x=-1+ 2 0.41 and x=-1- 2 -2.41 lie in [-3,1) . (2 solutions) Case x 1 : x^2+4x-3=0 x=-2 7 . Neither root 1 . (0 solutions) Total number of real solutions = 3 .