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<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 .