Algebra 1 3-6 Complete Lesson: Compound Inequalities

Last updated over 4 years ago

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A complete formative lesson with embedded slideshow, mini-lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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100

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Algebra 1 3-6 Complete Lesson: Compound Inequalities

Last updated over 4 years ago

36 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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. How much could the grower expect to earn in 1 year from 1 tree? Explain your reasoning.

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

-4 ≤ x < 6

-6 ≤ x < 4

6 < x ≤ -4

4 < x ≤ 6

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Problem 1 Got It? Graph the compound inequality that represents the phrase.
all real numbers that are greater than or equal to -4 and less than 6

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

6 ≤ x < 2.5

x ≤ 6 or x > 2.5

x ≤ -2.5 or x > 6

x ≤ 2.5 or x > 6

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Problem 1 Got It? Graph the compound inequality that represents the phrase.
all real numbers that are less than or equal to 2.5 or greater than 6

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

Problem 2 Got It? What are the solutions of -2 < 3y - 4 < 14? Graph the solutions.
Remember to write the simplified compound inequality before graphing the solutions on the number line.

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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.

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Problem 4 Got It? What are the solutions of -2y + 7 < 1 or 4y + 3 ≤ -5? Graph the solutions.
Remember to write the simplified compound inequality before graphing the solutions on the number line.

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

-2 > b ≥ 7

-2 < b ≤ 7

7 < b ≤ -2

-2 ≤ b < 7

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

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

[7, ∞)

(7, ∞)

(7, ∞]

[7, ∞]

What compound inequality represents the phrase "all real numbers that are greater than or equal to 0 and less than 8"? Write the inequality and graph the solutions on the canvas.

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What are the solutions of the compound inequality
Solve the inequality and graph the solutions on the canvas.

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Your test scores in science are 83 and 87. What possible scores can you earn on your next test to have a test average between 85 and 90, inclusive?

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Write the interval represented on the number line as an inequality.

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Write the interval represented on the number line in interval notation.

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Is this a compound inequality?

Yes

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Reasoning: What are the solutions of the inequalities as a compound inequality?

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Reasoning: What are the solutions of the compound in equality in interval notation?

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Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.
Categorize the sets.

{}
{1, 5}
{1, 3, 5, 7}
{4, 12}
{2, 4, 6, 8, 12, 15}
{5}

Subset of A
Subset of B
A'

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.
Is B' a subset of A?

Yes

Review Lesson 3-5: Solve the inequality.

n ≤ -3

n ≥ -3

n < 3

n ≤ 3

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Review Lesson 1-5: Complete each statement with <, =, or >.

|3 - 7| __?__ 4
|-5| + 2 __?__ 6
|6 - 2.5| __?__ 3.3

Vocabulary Review: Categorize each math sentence as an inequality or an equation.

15 > -12
18 ≤ 35
5x = 15
9 > 3x

Inequality
Equation

Vocabulary Review: Match the inequality symbol to its description. Not all inequlaity symbols will be used.

greater than
less than or equal to
greater than or equal to

Use Your Vocabulary: Identify the inequalities that are NOT compound inequalities. Select all that apply.

Use Your Vocabulary: Match each description on the left with the compound inequality it describes on the right.

all numbers less than 9 or greater than 5
all numbers less than 9 and greater than 5
all numbers less than 5 or greater than 9
all numbers less than 5 and greater than 9

Use Your Vocabulary: Which compound inequality from the previous item describes an empty set ?

all numbers less than 9 and greater than 5

all numbers less than 5 and greater than 9

all numbers less than 9 or greater than 5

all numbers less than 5 or greater than 9

100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

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Algebra 1 3-6 Complete Lesson: Compound Inequalities

Algebra 1 3-6 Complete Lesson: 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. How much could the grower expect to earn in 1 year from 1 tree? Explain your reasoning.

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

Problem 1 Got It? Graph the compound inequality that represents the phrase. 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.all real numbers that are less than or equal to 2.5 or greater than 6

Problem 1 Got It? Graph the compound inequality that represents the phrase. 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"?

Problem 2 Got It? What are the solutions of -2 < 3y - 4 < 14? Graph the solutions.Remember to write the simplified compound inequality before graphing the solutions on the number line.

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.Remember to write the simplified compound inequality before graphing the solutions on the number line.

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

What compound inequality represents the phrase "all real numbers that are greater than or equal to 0 and less than 8"? Write the inequality and graph the solutions on the canvas.

What are the solutions of the compound inequalitySolve the inequality and graph the solutions on the canvas.

Your test scores in science are 83 and 87. What possible scores can you earn on your next test to have a test average between 85 and 90, inclusive?

Write the interval represented on the number line as an inequality.

Write the interval represented on the number line in interval notation.

Is this a compound inequality?

Reasoning: What are the solutions of the inequalities as a compound inequality?

Reasoning: What are the solutions of the compound in equality in interval notation?

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.Categorize the sets.

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}. Is B' a subset of A?

Review Lesson 3-5: Solve the inequality.

Review Lesson 1-5: Complete each statement with <, =, or >.

Vocabulary Review: Categorize each math sentence as an inequality or an equation.

Vocabulary Review: Match the inequality symbol to its description. Not all inequlaity symbols will be used.

Use Your Vocabulary: Identify the inequalities that are NOT compound inequalities. Select all that apply.

Use Your Vocabulary: Match each description on the left with the compound inequality it describes on the right.

Use Your Vocabulary: Which compound inequality from the previous item describes an empty set ?

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

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. How much could the grower expect to earn in 1 year from 1 tree? Explain your reasoning.

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

Problem 1 Got It? Graph the compound inequality that represents the phrase. 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.all real numbers that are less than or equal to 2.5 or greater than 6

Problem 1 Got It? Graph the compound inequality that represents the phrase. 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"?

Problem 2 Got It? What are the solutions of -2 < 3y - 4 < 14? Graph the solutions.Remember to write the simplified compound inequality before graphing the solutions on the number line.

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.Remember to write the simplified compound inequality before graphing the solutions on the number line.

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

What compound inequality represents the phrase "all real numbers that are greater than or equal to 0 and less than 8"? Write the inequality and graph the solutions on the canvas.

What are the solutions of the compound inequalitySolve the inequality and graph the solutions on the canvas.

Your test scores in science are 83 and 87. What possible scores can you earn on your next test to have a test average between 85 and 90, inclusive?

Write the interval represented on the number line as an inequality.

Write the interval represented on the number line in interval notation.

Is this a compound inequality?

Is this a compound inequality?

Is this a compound inequality?

Is this a compound inequality?

Reasoning: What are the solutions of the inequalities as a compound inequality?

Reasoning: What are the solutions of the compound in equality in interval notation?

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.Categorize the sets.

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}. Is B' a subset of A?

Review Lesson 3-5: Solve the inequality.

Review Lesson 1-5: Complete each statement with <, =, or >.

Vocabulary Review: Categorize each math sentence as an inequality or an equation.

Vocabulary Review: Match the inequality symbol to its description. Not all inequlaity symbols will be used.

Use Your Vocabulary: Identify the inequalities that are NOT compound inequalities. Select all that apply.

Use Your Vocabulary: Match each description on the left with the compound inequality it describes on the right.

Use Your Vocabulary: Which compound inequality from the previous item describes an empty set ?

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Is this a compound inequality?

Is this a compound inequality?

Is this a compound inequality?

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

Problem 1 Got It? Graph the compound inequality that represents the phrase.
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.
all real numbers that are less than or equal to 2.5 or greater than 6

Problem 1 Got It? Graph the compound inequality that represents the phrase.
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.
Remember to write the simplified compound inequality before graphing the solutions on the number line.

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.
Remember to write the simplified compound inequality before graphing the solutions on the number line.

What are the solutions of the compound inequality
Solve the inequality and graph the solutions on the canvas.

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.
Categorize the sets.

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.
Is B' a subset of A?

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

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

Problem 1 Got It? Graph the compound inequality that represents the phrase.
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.
all real numbers that are less than or equal to 2.5 or greater than 6

Problem 1 Got It? Graph the compound inequality that represents the phrase.
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.
Remember to write the simplified compound inequality before graphing the solutions on the number line.

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.
Remember to write the simplified compound inequality before graphing the solutions on the number line.

What are the solutions of the compound inequality
Solve the inequality and graph the solutions on the canvas.

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.
Categorize the sets.

Review Lesson 3-5: Let A = {1, 3, 5, 7}, B = {4, 8, 12}, and let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 12, 15}.
Is B' a subset of A?

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.