Section 4.1 Solving Linear Inequalities Using the Addition-Subtraction Principle

4.1 Lecture Guide: Solving Linear Inequalities Using the Addition-Subtraction Principle Objective: Check possible solutions of an inequality.

Linear Inequalities Verbally A linear inequality in one variable is an inequality that is first degree in that variable. Algebraically For real constants A, B, and C, with Algebraic Examples Graphically ( 2 [ 2 ) 2 ] 2

1. Determine whether 4 or −4 is a solution of the inequality A solution of an inequality is a value that makes the inequality a true statement.

Objective: Use tables and graphs to solve linear inequalities in one variable.

2. The graph below displays the monthly cost y of two phone plans based on x minutes of use. The graph of represents the monthly cost of plan A and the graph ofrepresents the monthly cost of plan B. Minutes Cost (a) Approximate the monthly cost of plan A with 400 minutes of use. (b) Approximate the monthly cost of plan B with 400 minutes of use.

2. The graph below displays the monthly cost y of two phone plans based on x minutes of use. The graph of represents the monthly cost of plan A and the graph ofrepresents the monthly cost of plan B. Minutes Cost (c) Approximate the monthly cost of plan A with 800 minutes of use. (d) Approximate the monthly cost of plan B with 800 minutes of use.

2. The graph below displays the monthly cost y of two phone plans based on x minutes of use. The graph of represents the monthly cost of plan A and the graph ofrepresents the monthly cost of plan B. Minutes Cost (e) For how many minutes of use for will both plans have the same monthly cost? (f) What is that monthly cost?

2. The graph below displays the monthly cost y of two phone plans based on x minutes of use. The graph of represents the monthly cost of plan A and the graph ofrepresents the monthly cost of plan B. Minutes Cost (g) Explain the circumstances under which you would choose plan A. (h) Explain the circumstances under which you would choose plan A.

3. (a) (b) (c) Use the graph to solve each equation or inequality.

4. (a) (b) (c) Use the graph to solve each equation or inequality.

5. (a) (b) (c) Use the table to solve each equation or inequality.

6. (a) (b) (c) Use the table to solve each equation or inequality.

Objective: Solve linear inequalities in one variable using the addition-subtraction principle for inequalities.

Addition-Subtraction Principle for Inequalities Verbally Algebraically If a, b, and c, are real numbers then a < b is equivalent to andto Numerical Example is equivalenttoand to If the same number is added to or subtracted from both sides of an inequality, the result is an equivalent inequality.

Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 7.

8. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

9. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

10. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

11. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

12. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

13. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

14. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

15. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

16. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

17. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

18. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

19. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

20. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

21. Each inequality in problems 7-21 is a conditional inequality – an inequality that is true for some values of the variable and not true for others. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation.

22. Solve the inequalityby letting (a) Create a table on your calculator with the table settings: TblStart = 0; xY1Y1 Y2Y Complete the table below. Y 1 > Y 2 for x-values ____________ than ______. and

(b) Use your calculator to create a graph ofand using a viewing window of. Use the Intersect feature to find the point where these two lines intersect. Draw a rough sketch below. The values in the table will help. Y 1 is above Y 2 for x-values to the ____________ of ______. 22. Solve the inequalityby letting and

(c) Solve the inequalityalgebraically. (d) Do your solutions all match? 22. Solve the inequalityby letting and

Solve each inequality using only a graphing calculator:

25. Complete the following table. Can you give a verbal meaning for each case? PhraseInequality Notation Interval Notation Graphical Notation “x is at least 5” “x is at most 2” “x exceeds “x never exceeds ” ”

26. Write an algebraic inequality for the following statement, using the variable x to represent the number, and then solve for x. Verbal Statement: Five less than three times a number is at least two times the sum of the number and three. Algebraic Inequality: Solve this inequality:

Service A x Miles y $ Cost Service B x Miles y $ Cost The tables below display the charges for two taxi services based upon the number of miles driven. Service A has an initial charge of $2.30 and $0.15 for each quarter mile, while Service B has an initial charge of $2.00 and $0.20 for each quarter mile.

Service A x Miles y $ Cost Service B x Miles y $ Cost (a) Use these tables to solve Interpret the meaning of the solution in part (a).

Service A x Miles y $ Cost Service B x Miles y $ Cost (b) Use these tables to solve Interpret the meaning of the solution in part (b).

Service A x Miles y $ Cost Service B x Miles y $ Cost (c) Use these tables to solve Interpret the meaning of the solution in part (c).

28. The perimeter of the parallelogram shown must be greater than Find the possible valuesfor a. a a 8 8