How do you write an absolute value inequality that represents all real numbers less than 3 units from 0?

1 Answer
Jun 4, 2017

Answer:

#|x|<3#

Explanation:

#|x|# represents the distance away from 0 that a number is. Therefore, if we want to write an inequality representing all numbers that are a distance of less than 3 away from 0, we do it like this:

#|x|<3#

If we were to expand this, we would get the following inequality:

#-3 < x < 3#

Which makes sense, since both #-3# and #3# are a distance of #3# away from #0#, and everything in between them is closer to #0#.

Final Answer