please check answers and change if wrong thank you.

Question

The absolute value of 3 times a number x is greater than 33.

|3x| > 33
3x > 33
x > 11

what about -11

Answer 1

good question.
|x| = x if x>=0
So, your answer of 11 correctly solves
3x > 33

But, |x| = -x if x < 0
so, the other condition is

-3x > 33
x < -11

So, if x is farther than 11 units from 0, in either direction, 3x is farther than 33 units away from 0.

Answer 2

thank you very much for your help, anonymous. thanks ann