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

1 Answer
Jun 2, 2016

No, it does not have a solution.

Explanation:

#|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#.