Notes Packet #12 Grade 6 Mathematics Unit 4 Expressions and Equations Topic D Inequalities Name: Mrs. Archacki 1
Topic Objectives By the end of this topic you will be able to write inequalities. graph inequalities on a number line. solve one-step inequalities and graph the solutions on a number line. write, solve, and graph inequalities that represent real-world situations. Lesson #13 Introduction to Inequalities 2
Objective: By the end of this lesson, you will be able to write inequalities and graph inequalities on a number line. An inequality is a mathematical sentence that compares quantities. This Symbol < > Means Less than, fewer than More than, in excess of, exceeds Greater than or equal to, No more than, at most, maximum of Less than or equal to, No less than, at least, minimum of Example 1 Writing Inequalities a) The distance Mr. Chin drove was no more than 65 miles. b) The age of Mia s sister is less than 8 years. c) The temperature was at least 18 degrees. d) Leeza had at most four hundred dollars. * Helpful Hint you should ALWAYS read from the variabel AND put the variable on the left side of the inequality sign. * Lesson #13 - Practice A 3
Write an inequality for the word sentence. 1. Four people or fewer are allowed to ride at once. 2. Kristen has less than three days to write her paper. 3. You must deposit at least $20 to open a bank account. 4. An MP3 player can store less than 240 songs. 5. A ship can carry no more than 6 tons of cargo. 6. There are more than 15 ladybugs on the window sill. 7. After-school activities are cancelled at Kurt s school if there is at least 2.5 inches of snow. 8. The repairs to Ryan s bike costs more than $50. 9. Tabby s mom says that she must read for at least 30 minutes each night. 10. Phil has a $25 gift card to his favorite restaurant. Write an inequality showing how much Phil can spend at lunch. 11. People who are at least 12 years old must pay full price for a movie ticket. 12. You spend at most 2 hours studying for your math test. ***13. Ralph is five years younger than Paco. Together their age has a sum of at least 25. Write 2 inequalities showing the sum of Paco and Ralph Lesson #13 - Homework A 4
Directions: Write the inequality for the word sentence for #1-8 1) 18 more than a number is less than 29 2) The temperature t was at least 30 F 3) The amount of juice c is more than 3 cups 4) The number decreased by 29.8 is more than 139 5) An MP3 player can store less than 240 songs 6) 128 less than a number at most is 452 7) The product of a number and 6 is under 138 8) A ship can carry no more than 6 tons of cargo Directions: Write a word sentence to represent the inequality for #9-12. 9) n 23 10) 16 > p + 9 11) m < 139 y 12) 8 9 Lesson #13 - Extension 5
Directions: Write an EXPRESSION, EQUATION, and INEQUALITY for each situation. WATCH OUT FOR KEY WORDS! ( IS ) 1) A number plus 11 equals 48. Expression Equation Inequality 2) A number decreased by 9. Expression Equation Inequality 3) A number cubed is less than 64. Expression Equation Inequality 4) A number plus 7 is 33. Expression Equation Inequality 5) 18 less than a number is 19. Expression Equation Inequality 6) The sum of a number and 12 is at most 44. Expression Equation Inequality 7) 4 less than n is greater than 8. Expression Equation Inequality 8) The quotient of a number and 7 is at least 38. Expression Equation Inequality Example 2 Graphing Inequalities 6
- Inequalities are graphed on a number line. - When graphing inequalities, first determine if there will be an open or closed circle. - Then o Shade to the left if it is less than ( < ) or less than or equal to ( ) o Shade to the right if it is greater than ( > ) or greater than or equal to ( ) a) x < 6 c) p > 4 b) a 5 d) c 1 * Helpful Hints * - Always plot the point ON THE number line. - You must have an arrow at the end of your shading. - You must have AT LEAST FIVE values on your number line. - If the variable is on the left, the point on the inequality sign tells you the direction you need to shade. Lesson #13 Practice B 7
Graph each inequality on the number line. 1) a < 8 2) d 4 3) b 11 4) x > 3 5) x < 9 6) r 4 7) x > 10 8) x 6 9) x 2 10) x > 15 11) s < 6 12) b 13 13) x < 23 14) r > 18 15) r 5 16) x > 30 17) b 4 18) a 9 Lesson #13 - Homework Write an inequality AND graph for each sentence. 8
1. More than 2,500 people attended the convention. 2. Her earnings were no more than $64. 3. The winning 5K race time was less than 22 minutes. 4. A checking-account balance is no more than $500. 5. A maximum ceiling height of 8 feet was required in the new buildings. 6. A minimum number of 12 participants is required to hold a bike rally. 7. DONATIONS Total donations at the Fireman s Ball failed to reach $940. Write and graph an inequality that represents the amount raised. Lesson #14 Solving One Step Inequalities 9
Objective: By the end of the lesson, you will be able to solve one-step inequalities and graph the solution on a number line. Solving inequalities is similar to solving equations. The only difference is you must graph your solution on a number line. Recall To solve inequalities. Example Solve and graph the inequality. a) d + 5 > 11 b) 5 p 120 n c) 5 4 d) m 13 < 90 Lesson #14 Practice Solve and graph the solution to each equality. 10
1. 6 x > 12 2. h 4 > 9 n 3. s + 5 14 4. 4 3 5. m + 9 < 13 6. 2 q < 26 7. b 2 < 13 8. p 6 < 5 9. 13 b 39 10. w + 18 30 11
z 11. 8 3 12. y 5 < 12 s 13. 14 n 56 14. 2 < 1 6 15. TRANSPORTATION A certain minivan has a maximum carrying capacity of 1,200 pounds. The luggage weighs 150 pounds. Write and solve an inequality to find the maximum weight allowable for passengers. 16. DISCOUNTS To qualify for a store discount, Clay s soccer team must spend at least $560 for new jerseys. The team needs 20 jerseys. Write and solve an inequality to represent how much the team should spend on each jersey to qualify for the discount. Lesson #14 Homework 12
1) Solve and graph the solutions to the following inequalities. t a) 3r 36 c) 7 8 b) d 2 < 15 d) a + 10 < 14.6 2) Decide whether each statement is true or false. 3) A marathon runner plans to run at least 55 miles this week. He has already run 42 miles. The inequality represented by this situation is represented as 42 + m 55. Solve the inequality to find how many more miles he plans to run this week. Graph your solution on a number line. Lesson #15 Applications of Inequalities 13
Objective: By the end of this lesson, you will be able to write, solve, and graph inequalities that represent real-world situations. In this lesson, put your knowledge of writing, graphing, and solving inequalities together in order to solve real-world problems involving inequalities. Example 1 Spring cleaning has started and your parents offer you $3.00 an hour to go outside and clean up the yard. You want to earn at least $45.00 so you can take a friend to the movies this weekend to see Rio 2. Write an inequality to represent how much money you need to earn. Solve the inequality and graph your solution Example 2 The local girl scouts are hosting their first walk-a-thon. In order for the walk-a-thon to happen this year they need to raise at least $850.00. So far they have raised $375.00. Write an inequality to represent how much money they still need to raise. Solve the inequality to determine how much money they still need to raise. Graph your solution on a number line. Lesson #15 Practice 14
1. ENTERTAINMENT Gabe went to the amusement park with $40 to spend. His ticket cost $26.50. Write and solve an inequality to show how much he might spend on souvenirs and snacks. Graph your solution on a number line. 2. AQUARIUM Leeza s aquarium holds 55 gallons of water. She is filling the tank and has already put in 22 gallons. Write and solve an inequality to find out how many more gallons she might put in the tank. Graph your solution on a number line. 3. CARS Many mechanics advise people not to drive their cars more than 5,000 miles between oil changes. Kaci has driven her car 3,450 miles since the last oil change. Write and solve an inequality to find out how many more miles she might drive before having her oil changed again. Graph your solution on a number line. 4. FURNITURE Dan builds furniture. The table shows his minimum production times. Minimum Furniture Production Times (hr) Child's table 2 Bench 1 Dining table 4 China cabinet 7 Dan builds children s tables on Tuesday. He works 10 hours. Write and solve an inequality to determine how many children s tables Dan can build that day. Graph your solution on a number line. 5. PIANO Drew practices piano at least 45 minutes per day. He has already practiced 18 minutes. Write and solve an inequality to determine how much longer he will be practicing. Graph your solution on a number line. 6. SPORTS At baseball spring training, the coach throws at least 30 ground balls to each outfielder. He has thrown 16 ground balls to the right fielder. Write and solve an inequality to determine how many more balls he can be expected to throw to the right fielder. Graph your solution on a number line. Part E Review 15
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