How Do You Solve Absolute Value Inequalities with Double Variables?

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Discussion Overview

The discussion revolves around solving absolute value inequalities involving two variables. Participants explore the representation of inequalities when absolute value expressions are applied to both variables and the implications of different inequality signs.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant asks how to solve inequalities of the form |x| ± |y| =, >, <, a, particularly when both variables are involved.
  • Another participant notes that for |x| < a, the representation is -a < x < a, but questions how to express |x| ≤ a while considering both conditions simultaneously.
  • A different participant suggests dividing the problem into four conditions based on the signs of x and y, indicating that the solutions depend on these conditions.
  • One participant proposes that |x| ≤ a can be represented as -a ≤ x ≤ a, but reiterates the need for clarification on handling both inequalities together.

Areas of Agreement / Disagreement

Participants express uncertainty about how to represent absolute value inequalities with double variables, and there is no consensus on a single method or approach to solve these inequalities.

Contextual Notes

Participants mention a lack of examples in their text and that they have not been shown how to approach these problems in class, indicating potential gaps in foundational understanding.

h00zah
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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
 
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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.
 
h00zah said:
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 into 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
 
h00zah said:
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
h00zah said:
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.
 

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