Question

Which of the solution sets is all real numbers?
|x| < -1
|x| = -1
|x| > -1

Answer 1

The last one is all real number

Answer 2

The solution sets is all real numbers in case of:

|x| > -1

Explanation:

We know that modulus is a function with the property such that:

if a<0 then |a|= -a

that is the modulus of a negative number is positive and if a≥0

then |a| =a

and modulus of a positive value is also positive.

i.e. modulus function always gives positive value.

Hence,

1)

|x|<-1

This is not possible as modulus function always gives a value ≥0 for all real numbers.

2)

|x|= -1

This is also not possible as modulus of any number can't be negative.

3)

|x| > -1

The modulus of any number will definitely be greater than or equal to zero.

Hence, the solution set contain all the real numbers.