Unit 6 Inequalities. 17 (Late Start) Solving Inequalities with Mult. & Div. Section Solving Absolute Value Inequalities

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1 Unit 6 Inequalities Name The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay attention and make any necessary changes. All assignments are due the following class period unless indicated otherwise. Monday Tuesday Wednesday Thursday Friday December 15 (Pre-test) Writing & Graphing Inequalities 16 Calc. Quiz! Solving Inequalities with Addit. & Subtr. 17 (Late Start) Solving Inequalities with Mult. & Div. 18 Solving Multi-Step Inequalities 19 Solving Compound Inequalities Section Section Section 3.3 Section 3.4 Section 3.6a Review a Quiz a Vacation! Dec 24 Jan 4 January 5 Solving Compound Inequalities Section 3.6b 12 Unit 6 Review 6 Solving Absolute Value Equations Section 3.7a 13 Unit 6 Test 7 Solving Absolute Value Inequalities 8 Graphing Absolute Value Functions Section 3.7b Section More graphing & Unit 6 Review Semester Exams are January 20-22! Section Page Assignment from Algebra 1 Common Core (pearsonrealize.com) Score 3.1 p. 168 #8-42 even 3.2 p. 174 #10-50 even 3.3 p. 181 #8-48 even 3.4 p. 190 #11-16 all, 18, 21, 24, 27, 30, 33, 36, 39, 42, 44, 45, 47, 50, a p. 204 #9-22, all Quiz Review p. 193 & p. 193 #1-28 all & p. 225 #42-48 (solve and graph) p b --- worksheet or online assignment TBD 3.7a p. 211 #10-30 even, all 3.7b p. 211 #32-48 even, 57-60, p. 349 #6-11, all Unit 6 Review --- worksheet

2 Lesson 3.1 Writing and Graphing Inequalities Algebra Essential Question How can you use an inequality to describe a real-life statement? 1. Write an inequality for each statement. Then sketch the graph of the numbers that make each inequality true. a. Statement The temperature t in Sweden is at least 10 C. Inequality Graph b. Statement The elevation e of Alabama is at most 2407 feet. Inequality Graph 2. Write an inequality for each graph. Then, in words, describe all the values of x that make each inequality true. a. b. c. Communicate Your Answer 3. Write a real-life statement that involves each inequality. a. x > 3.5 b. x 6

3 Practice: Write the sentence as an inequality. 5. One-third of a number h is less than 15. Representing Linear Inequalities 6. Seven is less than or equal to the difference of a number q and The sum of a number u and 14 is more than 6. In Exercises 5 and 6, tell whether the value is a solution of the inequality. 8. d 7 12; d n 6; n 1 Graph the inequality. 10. x x < x Write an inequality that represents each graph.

4 Lesson 3.2 Solving Inequalities using Addition and Subtraction Algebra Essential Question How can you use addition or subtraction to solve an inequality? Work with a partner. The National Collegiate Athletic Association (NCAA) uses the following formula to rank the passing efficiencies P of quarterbacks. P 8.4Y 100C 330T 200N A Y total length of all completed passes (in Yards) C Completed passes T passes resulting in a Touchdown N intercepted passes A Attempted passes M incomplete passes 1. Work with a partner. Use the passing efficiency formula to create a passing record that makes each inequality true. Record your results in the table. Then describe the values of P that make each inequality true. Attempts Completions Yards Touchdowns Interceptions a. b. c. a. P 0 b. P c. P Exploration : 2. Solve. a. x + 3 = 4 b. x + 3 > 4 c. 4 = x - 2 d. 4 < x - 2

5 Practice Solve the inequality. Graph the solution h 4. s u c 3c p 8p You have $15 to spend on groceries. You have $12.25 worth of groceries already in your cart. a. Write an inequality that represents how much more money m you can spend on groceries. b. Solve the inequality.

6 Lesson 3.3 Solving Inequalities using Multiplication Algebra Essential Question How can you use division to solve an inequality? 6 > 4-8 < 6 10 > < (-3) (-2) Write a rule that describes how multiplication and division affect inequalities. 1. Solving Linear Inequalities Using Multiplication and Division Solve each inequality. Graph the solution. x (a) 2 2 (b) 3x 33 x (c) 2x 6 (d) 7 3 ( e) ¼ x > You earn $8.50 per hour at the sub shop. Write and solve an inequality that represents the number of hour you need to work to earn $187 to buy a tablet computer.

7 Lesson 3.4 Solving Multi-Step Linear Inequalities Algebra Essential Question How can you solve a multi-step inequality? 1. Solve each equation. (a) 2x 1 7 (b) 6x 11-2x 5 (c) 9( x 4) 7x 5(3x 2) (d) What rule must we follow when multiplying or dividing both sides of an inequality by a negative number? 2. Solving Multi-Step Linear Inequalities Solve each inequality. Then graph the solution. (a) 5x 3 12 (b) x x (c) x 1 3x 21 (d) 2x 4 4x x x

8 3. Application Exercises Write and solve an inequality to answer the question. Be sure to actually answer the question that is being asked. Geometry A rectangle is at least 36 square-feet. The length of the rectangle is 12 feet. Write an inequality that describes the possible width of the rectangle. x ft Area 36 ft 2 12 ft 4. You want to make a rectangular banner that is 18 ft long. You have no more than 48 ft of trim for the banner. What are the possible widths of the banner? a) Write the formula for the perimeter of a rectangle. b) Write an algebraic expression to describe the distance around a rectangular banner with a length of 18 ft and a width of w ft. c) Write an inequality to represent the situation described in the problem. Then solve your inequality. 5. Grades Your grade on 4 math tests are 79, 85, 86 and 88. What grade on your fifth test will give you a mean score of at least 85?

9 Lesson 3.6 Solving Compound Inequalities Algebra 1 Essential Question real number line? How can you use inequalities to describe intervals on the 1. Work with a partner. In parts (a) (d), use two inequalities to describe the interval. a. b. c. d. Do you use and or or to connect the two inequalities in parts (a) (d)? Explain. 2. Work with a partner. In parts (a) (d), use two inequalities to describe the interval. a. b. c. d. Do you use and or or to connect the two inequalities in parts (a) (d)?explain

10 1. Graphing Compound Inequalities Graph the Inequality. (a) The temperature ( F ) at which water is in a liquid state. (32 F < x < 212 F) Compound Inequalities A compound Inequality consist of two inequalities connect by and or or. All real numbers less than 0 or greater than x x (b) The temperature ( F ) at which water is not in a liquid state. (x < 32 F or x > 212 F) All real numbers greater than zero and less than or equal to x x 2. Solving Or Compound Inequalities Solve the inequality. Then graph the solution. 6x 5 7 or 8x x 3. Solving And Compound Inequalities Solve the inequality. Then graph the solution. 5 2x x 4. Reversing Both Inequality Symbols Solve the inequality. Then graph the solution x x 5. Setting up a compound inequality Since 1971, card players from around the world have been taking part in the main event of the World Series of Poker. Johnny Moss, the first winner of the event, earned a grand prize of $30,000. At the peak of the event s popularity in 2006, Jamie Gold won an astounding grand prize of $12,000,000. Write a compound inequality to represent the different grand prize amounts that players could have won from