Given, ∣x−2∣+∣x+2∣<4 Case I When x<−2⇒−(x−2)−(x+2)<4⇒−2x<4⇒−x<2⇒x>−2, which is not true. Hence, no value of x exist. Case II When −2<x<2⇒−(x−2)+x+2<4⇒4<4, which is not true. Hence, no value of x exist. Case III When x>2⇒x−2+x+2<4⇒2x<4⇒x<2, which is not true. Hence, no value of x exist. Hence, the number of solutions of the inequation is 0 .