More Absolute Value Inequalities

More Absolute Value Inequalities

Author: mary daunis

This tutorial illustrates the solution of the absolute value inequality


by several methods:

  • algebraic solution
  • graphical solution with TI graphing calculator
  • graphical solution with Geogebra

For an introduction to solving absolute value inequalities, please see the tutorial http://www.sophia.org/absolute-value-inequalities--2-tutorial

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Solving Algebraically

This video illustrates a simplified method for solving an absolute value inequality - what happens for x=3/8 is very interesting - notice that 3/8 is not included in a test interval but ends up in the solution interval! Can you figure out why this is so?

Graphical Solution - TI Graphing Calculator

Using the TABLE Function of TI Graphing Calculator

Using Geogebra

Actually, for the V-shaped absolute value graph one half is the line y=3x-1 broken at x = 0.5, and the other half is the line y=-3x+1. If you listen carefully you hear me say it incorrectly - just wanted to clear that up!