1. 2-1 © 2008 Pearson Prentice Hall. All rights reserved Chapter 2 Equations, Inequalities, and Problem Solving Active Learning Questions

2. 2-2 © 2008 Pearson Prentice Hall. All rights reserved Section 2.1 Linear Equations in One Variable Explain what is wrong with the following: a.) 5 should be added to both sides yielding 3x = 21. b.) Each side of the equation should first be divided by 3 yielding c.) The equation is correct. 3x – 5 = 16 3x = 11

3. 2-3 © 2008 Pearson Prentice Hall. All rights reserved Section 2.1 Linear Equations in One Variable Explain what is wrong with the following: a.) 5 should be added to both sides yielding 3x = 21. b.) Each side of the equation should first be divided by 3 yielding c.) The equation is correct. 3x – 5 = 16 3x = 11

4. 2-4 © 2008 Pearson Prentice Hall. All rights reserved Section 2.2 An Introduction to Problem Solving Suppose you are finding 112% of a number x. Which of the following is a correct description of the result? a.) The result is less than x. b.) The result is equal to x. c.) The result is greater than x.

5. 2-5 © 2008 Pearson Prentice Hall. All rights reserved Section 2.2 An Introduction to Problem Solving Suppose you are finding 112% of a number x. Which of the following is a correct description of the result? a.) The result is less than x. b.) The result is equal to x. c.) The result is greater than x.

6. 2-6 © 2008 Pearson Prentice Hall. All rights reserved Section 2.3 Formulas and Problem Solving Solve a.) b.) c.)

7. 2-7 © 2008 Pearson Prentice Hall. All rights reserved Section 2.3 Formulas and Problem Solving Solve a.) b.) c.)

8. 2-8 © 2008 Pearson Prentice Hall. All rights reserved Section 2.4 Linear Inequalities and Problem Solving Write {x | – 2 ≥ x} in interval notation. a.) (– ∞, – 2) b.) (– ∞, – 2] c.) [– 2, ∞)

9. 2-9 © 2008 Pearson Prentice Hall. All rights reserved Section 2.4 Linear Inequalities and Problem Solving Write {x | – 2 ≥ x} in interval notation. a.) (– ∞, – 2) b.) (– ∞, – 2] c.) [– 2, ∞)

10. 2-10 © 2008 Pearson Prentice Hall. All rights reserved Section 2.4 Linear Inequalities and Problem Solving Explain what is wrong with writing the interval (5, ∞]. a.) The ∞ symbol should come first, [∞, 5). b.) A parenthesis should be used to enclose ∞. c.) There is nothing wrong with this interval.

11. 2-11 © 2008 Pearson Prentice Hall. All rights reserved Section 2.4 Linear Inequalities and Problem Solving Explain what is wrong with writing the interval (5, ∞]. a.) The ∞ symbol should come first, [∞, 5). b.) A parenthesis should be used to enclose ∞. c.) There is nothing wrong with this interval.

12. 2-12 © 2008 Pearson Prentice Hall. All rights reserved Section 2.4 Linear Inequalities and Problem Solving In which of the following inequalities must the symbol be reversed during the solution process? a.) 2x – 3 < 10 b.) – x + 4 + 3x < 7 c.) – x + 4 < 5

13. 2-13 © 2008 Pearson Prentice Hall. All rights reserved Section 2.4 Linear Inequalities and Problem Solving In which of the following inequalities must the symbol be reversed during the solution process? a.) 2x – 3 < 10 b.) – x + 4 + 3x < 7 c.) – x + 4 < 5

14. 2-14 © 2008 Pearson Prentice Hall. All rights reserved Section 2.5 Compound Inequalities Given the graphs of M and N, which is true? a.) M  N = (– ∞, – 1] b.) M  N = (– ∞, 2] c.) M  N =  ] – 1 M:M: ) 2 N:N:

15. 2-15 © 2008 Pearson Prentice Hall. All rights reserved Section 2.5 Compound Inequalities Given the graphs of M and N, which is true? a.) M  N = (– ∞, – 1] b.) M  N = (– ∞, 2] c.) M  N =  ] – 1 M:M: ) 2 N:N:

16. 2-16 © 2008 Pearson Prentice Hall. All rights reserved Section 2.5 Compound Inequalities Which of the following is not a correct way to represent the set of all numbers between – 3 and 5? a.) {x | – 3 < x < 5} b.) – 3 < x or x < 5 c.) (– 3, 5)

17. 2-17 © 2008 Pearson Prentice Hall. All rights reserved Section 2.5 Compound Inequalities Which of the following is not a correct way to represent the set of all numbers between – 3 and 5? a.) {x | – 3 < x < 5} b.) – 3 < x or x < 5 c.) (– 3, 5)

18. 2-18 © 2008 Pearson Prentice Hall. All rights reserved Section 2.6 Absolute Value Equations Choose the value of c so that |x| – 7 = c has two solutions. a.) – 20 b.) – 7 c.) – 6

19. 2-19 © 2008 Pearson Prentice Hall. All rights reserved Section 2.6 Absolute Value Equations Choose the value of c so that |x| – 7 = c has two solutions. a.) – 20 b.) – 7 c.) – 6

20. 2-20 © 2008 Pearson Prentice Hall. All rights reserved Section 2.6 Absolute Value Equations True or false, absolute value equations always have two solutions. a.) True b.) False c.) It will depend on the variable.

21. 2-21 © 2008 Pearson Prentice Hall. All rights reserved Section 2.6 Absolute Value Equations True or false, absolute value equations always have two solutions. a.) True b.) False c.) It will depend on the variable.

22. 2-22 © 2008 Pearson Prentice Hall. All rights reserved Section 2.7 Absolute Value Inequalities Solve: |x| – 6 < – 1 a.) (– ∞, – 5)  (5, ∞) b.) (– 5, 5) c.) 

23. 2-23 © 2008 Pearson Prentice Hall. All rights reserved Section 2.7 Absolute Value Inequalities Solve: |x| – 6 < – 1 a.) (– ∞, – 5)  (5, ∞) b.) (– 5, 5) c.) 

24. 2-24 © 2008 Pearson Prentice Hall. All rights reserved Section 2.7 Absolute Value Inequalities Without taking any solution steps, how do you know that the absolute value inequality |3x – 2| > – 9 has a solution. What is the solution? a.) The absolute value is always nonnegative. (– ∞, ∞) b.) The absolute value is always nonnegative;  c.)  The absolute value is always 0; 

25. 2-25 © 2008 Pearson Prentice Hall. All rights reserved Section 2.7 Absolute Value Inequalities Without taking any solution steps, how do you know that the absolute value inequality |3x – 2| > – 9 has a solution. What is the solution? a.) The absolute value is always nonnegative. (– ∞, ∞) b.) The absolute value is always nonnegative;  c.)  The absolute value is always 0; 