If x is not equal to 0, is |x| less than 1?This is my most feared question type because it requires you to try out values but practice truly reduces that anxiety...
(1) x/|x| < x
(2) |x| > x
Test x=2: 1 < 2 (This works for the equation but |x| is not less than 1) NO!
Test x=-1/4: -1 < -1/4 (This works for the equation and |x| is less than 1) YES!
2. |x| > x
This means x is negative value.
x = -1: |x| is not less than 1 NO!
x = -1/4: |x| is less than 1 YES!
Together: We only test (-) values with x/|x| < x
So the only valid solution for x/|x| < x that is negative is a fraction.
Fractions are |x| less than 1. YES!
Impossible is nothing to God.