Solve |x| > -9. 1. no solution 2. all reals 3. x < -9 or x > 9

Question

Solve |x| > -9.

1. no solution
2. all reals
3. x

Answer 1

Answer: All reals

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

Answer 2

2. All reals

Explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see