Lesson 3
1. Lesson 3
1.10. Explore 6
Module 7: Absolute Value and Reciprocal Functions
Solving Problems Involving Absolute Value Equations
Absolute value equations can be used to model and solve problems dealing with the concept of tolerances. Tolerance is the amount of variation allowed in the measure of a quantity. Work through the next Try This activity to see an example.
Try This 2
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A ballistic vest is used to protect a person from injury by bullets. Typically worn by police officers in potentially hostile territory, these vests are subjected to strict testing to ensure safety and quality. In most cases, the performance of a ballistic vest is judged to be greater as it is able to withstand bullets fired at higher velocities. For example, a Type II vest protects against 9-mm bullets travelling at a speed of 398 m/s ± 9 m/s.
- Write an absolute value equation that can be used to determine the greatest and least velocities allowed.
- Solve the equation. What is the greatest velocity allowed? What is the least velocity allowed?
- With what other methods could you solve this problem?
Save your responses in your course folder.
Turn to “Example 2” on pages 383–384 to see how a different, but related, problem can be solved by an absolute value equation. As you read, focus on the two methods that are presented. How do you know if the solutions are reasonable?
Share 3
A good way to check your understanding of the concepts presented in this lesson is to analyze the work of another student. With a partner, turn to the following questions in your textbook. Discuss any errors in the solution. Copy the equation and show the correct work with the correct solution.
- Go to page 390 and answer question 15.
- Go to page 413 and answer question 9.
Record your answers in your course folder.
Self-Check 4
Turn to pages 389–391 of your textbook to practise applying the concepts that you have learned. Complete questions 9, 11, and 23. Check the solutions in the back of the textbook to make sure you are doing the questions correctly. You may also want to review relevant parts of the lesson as you work through the questions. Answer