1. Lesson 3

1.7. Explore 3

Mathematics 20-1 Module 7

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.

 

This shows an illustration of a number line with a red arrow pointing from –6 to 0, and a blue arrow pointing from 6 to 0.

This is a play button for the Absolute Value Equations applet.

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.

  1.  Answer

  2.  Answer