Lesson 3
1. Lesson 3
1.7. Explore 3
Module 7: Absolute Value and Reciprocal Functions
Solving Absolute Value Equations Algebraically
Recall the piecewise definition of an absolute value expression 
:
This notation implies that there are two cases to consider when evaluating an absolute value expression depending on the sign of the expression contained by the absolute value symbol.
Similarly, you need to be aware that there may be more than one possible solution when solving an absolute value equation.
Consider the equation 
. Recall that the definition of an absolute value number is the number’s distance from zero on a number line. Since 
and 
, the roots of the equation are 6 and −6.
Recall the activity in the Discover section. In that exercise you solved the equation 
. You can approach this equation in the same way as solving 
. Work through the “Absolute Value Equations” applet to see how this is done. Select the Tutorial icon, and then select “Solving: Algebraically.”
Self-Check 2
Use a personal strategy to solve the following absolute value equations.
