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

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infinite

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Solution

The correct option is D 0
We have the inequality $| x - 2 | + | x + 2 | < 4$

Case 1: $x \leq - 2$ , the equation becomes $2 - x - 2 - x < 4 ⟹ x > 0$ . Hence NO SOLUTIONS as $x \leq - 2$

Case 2: $- 2 < x \leq 2$ , the equation becomes $2 - x + x + 2 < 4 ⟹ 4 < 4$ . Hence NO SOLUTIONS

Case 3: $x > 2$ , the equation becomes $x - 2 + x + 2 < 4 ⟹ x < 2$ . Hence NO SOLUTIONS as $> 2$

Therefore, there are NO SOLUTIONS for the given inequality

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