Which of the solution sets is all real numbers?
|x| < -1, |x| = -1, |x| > -1, None of the above

Solution:

A modulus is a function with property

If a<0 then |a| = -a

This means that the modulus of a negative number is positive

If a ≥0 then |a| = a

This means that the modulus of a positive number is positive.

Now considering the options given,

(1) |x| < -1

It is not possible as the modulus function provides a value that is greater than or equal to 0 for all real numbers.

(2) |x| = -1

It is not possible as the modulus of any number cannot be negative.

(3) |x| > -1

The modulus of any number is greater than or equal to zero.

Therefore, |x| > -1 is all real numbers.

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Which of the solution sets is all real numbers?

Summary:

In |x| > -1, the solution set is all real numbers.