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

Answer 1

#|x|<3#

#|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

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Answer 2

Genesis Allen

The absolute value inequality that represents all real numbers less than 3 units from 0 is:

| x | < 3

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.