# Absolute value inequalities

## Main Question or Discussion Point

how do you go about solving abs value inequalities with double variables when the abs value bars are on both the variables?

eg; |x| + or - |y| =, >, <, a

I know that when |x| < a it must be -a < x < a, but when |x| "is less than or equal to" a, how do you represent both rules at once?

this is not h.w, we're doing this in class and we haven't been shown how to do this and there are no examples in my text.

but when |x| "is less than or equal to" a, how do you represent both rules at once?
You don't
You divide the problem in to n regions/conditions.
In this problem it is four conditions; x and y , positive and negative.

Then the interval solutions depend on the condition/region.

Check out
http://www.purplemath.com/modules/absineq.htm

Mark44
Mentor
I know that when |x| < a it must be -a < x < a, but when |x| "is less than or equal to" a, how do you represent both rules at once?
Like this: -a <= x <= a
this is not h.w, we're doing this in class and we haven't been shown how to do this and there are no examples in my text.