Question

The number of solutions of the inequation $|x-2|+|x+2|<4$ is

• A. $1$
• B. $2$
• C. $4$
• D. $0$
• E. $3$

Answer 1

The correct option is D

$0$

Find the number of solutions of the given inequation

Given, $|x-2|+|x+2|<4$

Case 1: when $x\le -2$,

the equation becomes $2-x-2-x<4$

$⟹x>0$

Therefore, there's no solution when $x\le -2$

Case 2: when $-2<x\le 2$,

the equation becomes $2-x+x+2<4$

$⟹4<4$

Therefore, there's no solution when $-2<x\le 2$

Case 3: when$x>2$,

the equation becomes$x-2+x+2<4$

$⟹⟹x<2$

Therefore, there's no solution when $x>2$

Hence, option (D) is the correct answer.