Problem 1 Got It? What is the difference between "x is between -5 and 7" and "x is between -5 and 7, inclusive"?
10
Question 17
17.
Take Note: Describe two techniques for solving and-type compound inequalities.
10
Question 19
19.
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.
Question 20
20.
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.
5
5
Question 23
23.
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.
Question 24
24.
Question 25
25.
Question 26
26.
Problem 5 Got It? What is the graph of (-2, 7]?
Question 27
27.
Question 28
28.
Problem 5 Got It? What is the graph of (3, \infin)?
10
Question 29
29.
Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?
Question 1
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 minimum amount the grower should expect to earn in 1 year from 1 tree? Enter only a dollar amount in this format: $17.29
Question 2
2.
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
Question 3
3.
Solve It! Explain how you found the maximum and minimum amounts on the previous items.
Question 4
4.
Take Note: Define compound inequality. You may use the canvas to illustrate your definition.
Question 5
5.
Take Note: Describe the graph of a compound inequality that uses the word and. You may use the canvas to illustrate your description.
Question 6
6.
Take Note: Describe the graph of a compound inequality that uses the word or. You may use the canvas to illustrate your description.
Question 7
7.
Take Note: Describe the process of rewriting an "and-type" compound inequality from two individual inequalities. You may include an example.
Question 8
8.
Take Note: Combine the two inequalities below into one simplified compound inequality.
-3<x and x\leq5
Question 9
9.
Take Note: Describe what inclusive means in phrases like the one below.
between 1 and 10, inclusive
Question 10
10.
Question 11
11.
Take Note: What do you think exclusive means in phrases like the one below.
between 1 and 10, exclusive
Question 12
12.
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
-6 ≤ x < 4
6 < x ≤ -4
4 < x ≤ 6
-4 ≤ x < 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
x ≤ -2.5 or x > 6
6 ≤ x < 2.5
x ≤ 2.5 or x > 6
x ≤ 6 or x > 2.5
Question 18
18.
Take Note: At this point, which of the two techniques for solving and-type compound inequalities do you prefer? Explain.
Question 21
21.
Question 22
22.
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?
-2 > b ≥ 7
-2 < b ≤ 7
7 < b ≤ -2
-2 ≤ b < 7
Problem 5 Got It? How do you write y > 7 in interval notation?
[7, ∞]
(7, ∞)
(7, ∞]
[7, ∞)
Take Note: Which inequality symbols are used to represent inclusive?
< and >
\leq and \geq
Take Note: Which inequality symbols are used to represent exclusive?
< and >
\leq and \geq
Take Note: In which type of compound inequality must solutions satisfy both of the individual inequalities?
or-type
and-type
Take Note: In which type of compound inequality must solutions only satisfy one of the individual inequalities?
