Algebra 1 3-6 Guided Practice: Compound Inequalities

Solve It! The diagram shows the number of boxes of oranges that an orange tree can produce in 1 year. An orange grower earns $9.50 for each box of oranges that he sells. What is the minimum amount the grower should expect to earn in 1 year from 1 tree? Enter only a dollar amount in this format: $17.29

A.REI.3

A.CED.1

Solve It! The diagram shows the number of boxes of oranges that an orange tree can produce in 1 year. An orange grower earns $9.50 for each box of oranges that he sells. What is the maximum amount the grower should expect to earn in 1 year from 1 tree? Enter only a dollar amount in this format: $17.29

A.REI.3

A.CED.1

Solve It! Explain how you found the maximum and minimum amounts on the previous items.

A.REI.3

A.CED.1

Take Note: Define compound inequality. You may use the canvas to illustrate your definition.

Take Note: Describe the graph of a compound inequality that uses the word and. You may use the canvas to illustrate your description.

Take Note: Describe the graph of a compound inequality that uses the word or. You may use the canvas to illustrate your description.

Take Note: Describe the process of rewriting an "and-type" compound inequality from two individual inequalities. You may include an example.

Take Note: Combine the two inequalities below into one simplified compound inequality.
-3<x and x\leq5

Take Note: Describe what inclusive means in phrases like the one below.

between 1 and 10, inclusive

Take Note: Which inequality symbols are used to represent inclusive?

Take Note: What do you think exclusive means in phrases like the one below.

between 1 and 10, exclusive

Take Note: Which inequality symbols are used to represent exclusive?

Take Note: In this course, if an and-type compound inequality contains neither inclusive nor exclusive, you can assume that it is exclusive. 

For example, "between 5 and 7" can be interpreted as "between 5 and 7, exclusive" 
or 5<x<7. 
The boundaries 5 and 7 are NOT included in the set. 

Take Note: Each compound inequality graphed on the right is the result of combining two of the individual inequalities whose graphs are shown on the left. Categorize the individual inequalities from the left appropriately.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

The two graphs whose inequalities combine to form the and-type compound inequality graphed here.
The two graphs whose inequalities combine to form the or-type compound inequality graphed here.

Problem 1 Got It? Write a compound inequality that represents the phrase. Also, graph the compound inequality that represents the phrase on the canvas.

all real numbers that are greater than or equal to -4 and less than 6

A.REI.3

Problem 1 Got It? Write a compound inequality that represents the phrase. Also, graph the compound inequality that represents the phrase on the canvas.

all real numbers that are less than or equal to 2.5 or greater than 6

A.REI.3

Problem 1 Got It? What is the difference between "x is between -5 and 7" and "x is between -5 and 7, inclusive"?

Take Note: Describe two techniques for solving and-type compound inequalities.

Take Note: At this point, which of the two techniques for solving and-type compound inequalities do you prefer? Explain.

Problem 2 Got It? What are the solutions of -2 < 3y - 4 < 14? Graph the solutions. Show your steps on the canvas as well.

You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.REI.3

Problem 3 Got It? Reasoning: Suppose you scored 78, 78, and 79 on the first three tests. Is it possible for you to earn a B in the course? Explain.

Recall that in this scenario Bs represent grades of 84 - 86, inclusive.
Assume that 100 is the maximum grade that you can earn in the course.

A.CED.1

A.REI.3

Take Note: In which type of compound inequality must solutions satisfy both of the individual inequalities?

Take Note: In which type of compound inequality must solutions only satisfy one of the individual inequalities?

Problem 4 Got It? What are the solutions of -2y + 7 < 1 or 4y + 3 ≤ -5?
Graph the solutions.

Show your steps on the canvas as well.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.REI.3

Take Note: Classify each inequality symbol and interval notation symbol based on its type.

≤
>
≥
)
<
(
[
]

Inclusive (includes boundaries)
Exclusive (excludes boundaries)

Problem 5 Got It? How do you write (-2, 7] as a compound inequality?

A.REI.3

Problem 5 Got It? What is the graph of (-2, 7]?

A.REI.3

Problem 5 Got It? How do you write y > 7 in interval notation?

Problem 5 Got It? What is the graph of (3, \infin)?

A.REI.3

Solve It! Explain how you found the maximum and minimum amounts on the previous items.

Take Note: Define compound inequality. You may use the canvas to illustrate your definition.

Take Note: Describe the graph of a compound inequality that uses the word and. You may use the canvas to illustrate your description.

Take Note: Describe the graph of a compound inequality that uses the word or. You may use the canvas to illustrate your description.

Take Note: Describe the process of rewriting an "and-type" compound inequality from two individual inequalities. You may include an example.

Take Note: Combine the two inequalities below into one simplified compound inequality.-3<x and x\leq5

Take Note: Describe what inclusive means in phrases like the one below.between 1 and 10, inclusive

Take Note: Which inequality symbols are used to represent inclusive?

Take Note: What do you think exclusive means in phrases like the one below.between 1 and 10, exclusive

Take Note: Which inequality symbols are used to represent exclusive?

Problem 1 Got It? Write a compound inequality that represents the phrase. Also, graph the compound inequality that represents the phrase on the canvas.all real numbers that are greater than or equal to -4 and less than 6

Problem 1 Got It? Write a compound inequality that represents the phrase. Also, graph the compound inequality that represents the phrase on the canvas.all real numbers that are less than or equal to 2.5 or greater than 6

Problem 1 Got It? What is the difference between "x is between -5 and 7" and "x is between -5 and 7, inclusive"?

Take Note: Describe two techniques for solving and-type compound inequalities.

Take Note: At this point, which of the two techniques for solving and-type compound inequalities do you prefer? Explain.

Problem 2 Got It? What are the solutions of -2 < 3y - 4 < 14? Graph the solutions. Show your steps on the canvas as well. You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 3 Got It? Reasoning: Suppose you scored 78, 78, and 79 on the first three tests. Is it possible for you to earn a B in the course? Explain.Recall that in this scenario Bs represent grades of 84 - 86, inclusive.Assume that 100 is the maximum grade that you can earn in the course.

Take Note: In which type of compound inequality must solutions satisfy both of the individual inequalities?

Take Note: In which type of compound inequality must solutions only satisfy one of the individual inequalities?

Problem 4 Got It? What are the solutions of -2y + 7 < 1 or 4y + 3 ≤ -5? Graph the solutions.Show your steps on the canvas as well.You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Take Note: Classify each inequality symbol and interval notation symbol based on its type.

Problem 5 Got It? How do you write (-2, 7] as a compound inequality?

Problem 5 Got It? What is the graph of (-2, 7]?

Problem 5 Got It? How do you write y > 7 in interval notation?

Problem 5 Got It? What is the graph of (3, \infin)?

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Combine the two inequalities below into one simplified compound inequality.
-3<x and x\leq5

Take Note: Describe what inclusive means in phrases like the one below.

between 1 and 10, inclusive

Take Note: What do you think exclusive means in phrases like the one below.

between 1 and 10, exclusive

Problem 1 Got It? Write a compound inequality that represents the phrase. Also, graph the compound inequality that represents the phrase on the canvas.

all real numbers that are greater than or equal to -4 and less than 6

Problem 1 Got It? Write a compound inequality that represents the phrase. Also, graph the compound inequality that represents the phrase on the canvas.

all real numbers that are less than or equal to 2.5 or greater than 6

Problem 2 Got It? What are the solutions of -2 < 3y - 4 < 14? Graph the solutions. Show your steps on the canvas as well.

You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

Problem 3 Got It? Reasoning: Suppose you scored 78, 78, and 79 on the first three tests. Is it possible for you to earn a B in the course? Explain.

Recall that in this scenario Bs represent grades of 84 - 86, inclusive.
Assume that 100 is the maximum grade that you can earn in the course.

Problem 4 Got It? What are the solutions of -2y + 7 < 1 or 4y + 3 ≤ -5?
Graph the solutions.

Show your steps on the canvas as well.
You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.