1. Lesson 3

1.4. Discover

Mathematics 20-1 Module 7

Module 7: Absolute Value and Reciprocal Functions

 

Discover
 

This shows an illustration of a green cylinder casting a shadow across a 5 x 5 checkerboard. The checkerboard is made up of squares of two different shades of grey. There are two yellow circle on two of the squares.

 

Are the circles in the illustration different colours, or are they the same colour?

 

In this section you will investigate the solutions of absolute value equations.

 

Try This 1

 

Part A

 

Consider the equation = 6.

  1. Is the root of the equation x + 1 = 6 also a root of the equation = 6?

  2. Think of another value of x that satisfies the equation = 6.

  3. Solve = 6 by graphing with or without technology.

  4. Does the solution match your answers from questions 1 and 2?

Part B

 

Consider the equation = 2x.

  1. Is the root of the equation x − 6 = 2x also a root of the equation = 2x?

  2. Solve this equation by graphing with or without technology. hint

  3. How can you obtain the solution from question 6 using an algebraic approach?

course folder Save your answers in your course folder.

 

Share 1

 

With a classmate, discuss the following questions. Record your responses.

  1. What are the differences when solving absolute value equations graphically and algebraically?

  2. How would you instruct someone to solve an absolute value equation algebraically? What tips would you give?

  3. Why do you think algebraic solutions sometimes lead to extraneous solutions?

course folder Save your responses in your course folder.

Remember that you can solve two equations, x − 6 = 2 and −x + 6 = 2.
You can graph x + 1 = 6 and −x − 1 = 6.