Linear Inequalities and Systems of Linear Inequalities

Common Core Standards:

MCC9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions.

MCC9-12.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable in a modeling context.

MCC9-12.A.REI.12 Graph the solution to a linear inequality in two variables as half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Objective: Students will write linear inequalities and systems of linear inequalities in two variables and graph the solutions given different information such as inequalities, systems of inequalities and word problems.

Procedure: This activity could be used as a whole group activity, in stations or centers, in small groups, or as a formative assessment. This can be used as separate worksheets or placed on cards. The teacher may want to provide graph paper.

Differentiation Options:This activity is designed for differentiation. Each set of problems is designed at specific levels of difficulty. You can build your own sets based on students’ ability levels.

Extension: He Shoots! He Scores! Worksheet

Level 1 Problems:

Solve the inequality. (Differentiation Strategy: You could only use inequalities that are in slope-intercept form or use all inequalities that are not in slope-intercept form.)

1. y ≤ x + 2 2. y ≤ 3

3. y > 5 4. x + 2y ≥ 6

5. -2x + 3y < -6 6. 2x + 5y ≥ -20

Level 2 Problems:

Write an inequality based on each given scenario. Then solve the inequality. (Differentiation Strategy: Students could just write the inequality.)

1. You receive an $80 gift card to the bookstore. Hardback books cost $8 and paperback books cost $4. How many books of each type can you buy?

2. A catering company has small tables and large tables. Small tables seat 4 people and large tables seat 6. They are planning a party for 100 guests. How many of each size table can they use?

3. You and your friend have $14 among you to spend on snacks at the basketball game. If drinks are $2 and popcorn is $1, how many of each can you purchase?

4. Sam wants to purchase birthday gifts for his two sisters that share the same birthday. One sister likes daisies which cost $2 per stem and the other likes tulips which cost $3 per stem. If he has $12 to spend, how many of each could he buy?

5. The fair is in town and you have earned $50 from math tutoring and want to go. If each ride is $2.50 and each game is $2, how many of each can you participate in during your visit?

Level 3 Problems:

Solve the system of inequalities. (Differentiation Strategy: You could only use inequalities that are in slope-intercept form or use all inequalities that are not in slope-intercept form.)

1. y ≥ -5x + 4 2. y ≤ x - 3 y > -2 y ≥ -x – 1

3. y > 4x – 5 4. y < -2 y ≥ -2x + 3 x + y ≥1

5. x + y ≥ -3 6. 3x + y ≥ -2 x + y ≤ 3 x ≤ 4 – 2y

Level 4 Problems:

Write a system of inequalities based on each given scenario. Then solve the system of inequalities. (Differentiation Strategy: Students could just write the system of inequalities or the teacher could have part of the inequalities written leaving only some of the pieces for the students to complete.)

1. You can work at most 25 hours next week. You need to earn at least $85 to cover your gas and food expenses. Your babysitting job pays $7.50 per hour and your math tutoring job pays $6 per hour. Write a system of linear inequalities to model the situation and then solve.

2. Mandy is buying plants and soil for a flowerbed for her mom. The soil costs $5 per bag and the plants cost $12 each. She wants to buy at least 6 plants and can spend no more than $100. Write a system of linear inequalities to model the situation and then solve.

3. Josh is going to the store to buy candy. Bags of candy corn cost $3 and bags of chocolate cost $5. He needs to buy at least 20 bags of candy and he cannot spend more than $60. Write a system of linear inequalities to model the situation and then solve.

4. Jenny is packing dishes into boxes. Each box can hold either 15 small plates or 8 large plates. She needs to pack at least 9 boxes and at least 150 plates. Write a system of linear inequalities to model the situation and then solve.

5. The band is selling boxes of fruit to raise money for new uniforms. Boxes of oranges cost $12 per box and boxes of grapefruits cost $15 per box. To get free shipping on all of the fruit each band member must sell at least 25 boxes of fruit. In order to meet your goal, you want to sell at least $500 worth of fruit. Write a system of linear inequalities to model the situation and then solve.

He Shoots! He Scores!

When Bo got home from his basketball game last night, looking pretty pleased with himself, his roommates asked how it went. He said that he had 10 rebounds, 2 blocks, 3 assists, and equaled or bettered his season high in points. Naturally they wanted to know exactly how many points he scored. Since he never likes to give them a straight answer, he told them the following:

I didn’t shoot any free throws. The number of 2-point baskets I made is more than twice the number of 3-point

baskets I made. The number of 2-pointers I made is less than or equal to 8. My previous season high was 18 points.

Now the roommates had to do some thinking! Let’s see if you can figure it out.

1. Using t to represent the number of 3-pointers he made, g to represent the number of 2-pointers, and f to represent the number of free throws, write equations or inequalities to represent all of the information given above. (Hint: You should have 4 statements.)

2. Graph each of the inequalities or equations.

3. What are all of the possible points for Bo?