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

Question

anonymous · Answer

hi Welcome to Openstudy!

I think it would be $|x<3|$ because absolute start at zero (depending on the inequality) and it can not be negative.

anonymous · Answer

can you tell me why it wouldn't be -3<x<3?

anonymous · Answer

thank you for helping :-)

anonymous · Answer

oh yeah you are right sorry. (i keep doing mistakes tonight)
$|x| <3 $, which is also the same as -3<x<3

anonymous · Answer

because any value for |x| less than three, will still be positive and it is above zero

anonymous · Answer

so then all numbers more than 7.5 units from 0 would be x<-7.5 OR x>7.5?

anonymous · Answer

|x| > 7.5 
same as x > -7.5 or x> 7.5

anonymous · Answer

so i'm on the right track?  i'm trying to help my daughter with her 8th grade homework :-(

anonymous · Answer

so Ix+2I>6 would be for all numbers more than 2 units from 6?

anonymous · Answer

yes you are on the right track :)

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