Chapter 1: Section 6 Notes
By the end of the section, you should be able to:
- Solve absolute value equations and inequalities.
- Create absolute value equations and inequalities to model situations.
Definitions:
- Absolute Value: the distance a real number x is away from zero.
- Extraneous Solution: a solution found from an original equation that is not a solution to the original equation.
Absolute Value Notation
The absolute value of x is written using the notation: |x|
Solving Absolute Value Equations
Things/Steps to Remember:
- When solving absolute value equations ALWAYS get the absolute value by itself on one side of the equation FIRST.
- Once the absolute value is isolated create two equations
- The absolute value set equal to the rest of the equation
- The absolute value set equal to the OPPOSITE of the rest of the equation (multiply a negative through)
- DO NOT move anything outside of the absolute value bars unless you have split the absolute value into two equations.
- When moving parts from one side of an equation to the other work furthest away from the absolute value first. In example 1 we moved the 3 (addition/subtraction) first, then we moved the 2 (multiplication/division).
- Remember to check your solution(s) in the original equation (the equation given in the problem)
Solving Absolute Value Inequalities
Things/Steps to Remember:
- If an absolute value is less than a number, then an AND compound inequality is formed.
- If an absolute value is greater than a number, then an OR compound inequality is formed.
Modeling using Absolute Value Equations/Inequalities
Things/Steps to Remember:
- Absolute value shows the distance away from zero. This function is helpful for finding the distance away from any number with a little modification as we showed in Example 5.
Section 1.6 Worksheet |
Section 1.6 WS Answers |
If you had any problems with the example videos on this page, or have any comments to make them better, please click the button below.