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Does the inequality |x + 1| < 0 has a solution?

Answer 1

No, it does not have a solution.

#|a|# is absolute value of #a# i.e. if #a# is positive than #|a|# is nothing but #a#. But if #a# is negative, #|a|# is the number itself without its negative sign i.e. only positive #a#. In other words if #a# is negative, #|a|=-a#.

Hence #|a|# is always positive and the lowest value can only be #0#. Hence, it is not possible to have absolute value of any number to be negative as absolute value is always greater than or equal to one and hence there is no solution for #|x+1|<0#.

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Answer 2

Roman Alvarez

No, the inequality |x + 1| < 0 does not have a solution.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Does the inequality |x + 1| &lt; 0 has a solution?

Does the inequality |x + 1| < 0 has a solution?