Section 4.1 Solving Linear Inequalities Using the Addition-Subtraction Principle
4.1 Lecture Guide: Solving Linear Inequalities Using the Addition-Subtraction Principle Objective 1: Identify linear inequalities and check a possible solution of an inequality.
VerballyAlgebraicallyAlgebraic Examples Graphically A linear inequality in one variable is an inequality that is ____________ degree in that variable. For real constants A, B, and C, with.. ( 2 [ 2 ) 2 ] 2 Linear Inequalities
1. Which of the following choices is a linear inequality in one variable? (a)(b)(c)(d)
A conditional inequality contains a variable and is true for ____________, but not all, real values of the variable. The solution of a linear inequality consists of all values that ____________ the inequality. The solution of a conditional linear inequality will be an interval that contains an infinite set of values. Conditional Inequality
2. Determine whether x = 5 satisfies each inequality. (a) (b)(c)(d)
3. Determine whether either 4 or – 4 satisfies the inequality.
Objective 2: Solve linear inequalities in one variable using the addition-subtraction principle for inequalities. VerballyAlgebraicallyNumerical Example If the same number is ____________ to or subtracted from ____________ sides of an inequality, the result is an ___________ inequality. If a, b, and c, are real numbers then a < b is equivalent to and to is equivalent to and to. Addition-Subtraction Principle for Inequalities
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 12.
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 13.
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 14.
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 15.
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 16.
Each inequality in problems 4-17 is a conditional inequality. Use the addition-subtraction principle of equality to solve each inequality. Give your answer in interval notation. 17.
18. 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 of represents 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. Objective 3: Use tables and graphs to solve linear inequalities in one variable.
(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. 18. 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 of represents the monthly cost of plan B. Minutes Cost
(e) For how many minutes of use will both plans have the same monthly cost? (f) What is that monthly cost? 18. 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 of represents 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 B. 18. 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 of represents the monthly cost of plan B. Minutes Cost
19. (a) (b) (c) Use the graph to solve each equation or inequality.
20. Use the graph to solve each equation or inequality. (a) (b) (c)
21. Use the table to solve each equation or inequality. (a) (b) (c)
22. Use the table to solve each equation or inequality. (a) (b) (c)
(a) Use your calculator to create a graph of and 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. is above for x-values to the ____________ of ______. 23. Solve the inequality by letting and. (b)
(c) Create a table on your calculator with the table settings: TblStart = 0;. Complete the table below for x-values ______ than ______. 23. Solve the inequality by letting and.
(d) (e) Do your solutions all match? Solve the inequality algebraically. 23. Solve the inequality by letting and.
Solve each inequality algebraically or graphically. 24.
25. Solve each inequality algebraically or graphically.
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. (a) Use these tables to solve (b) (c) (d) Interpret the meaning of the solution in parts (a) – (c).
27. 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 is smaller than ” ”
28. 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:
a cm 8 cm 29. The perimeter of the triangle shown must be less than 26 cm. Find the possible values for a.