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Algebra 1 3-6 Complete Lesson: Compound Inequalities

By Matt Richardson
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Last updated about 2 years ago
36 Questions
Note from the author:
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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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. How much could the grower expect to earn in 1 year from 1 tree? Explain your reasoning.
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2.
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
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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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4.
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
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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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6.
Problem 1 Got It? What is the difference between "x is between -5 and 7" and "x is between -5 and 7, inclusive"?
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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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10.
Problem 5 Got It? How do you write (-2, 7] as an inequality?
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Problem 5 Got It? What is the graph of (-2, 7]?
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12.
Problem 5 Got It? How do you write y > 7 in interval notation?
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13.
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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14.
What are the solutions of the compound inequality
Solve the inequality and graph the solutions on the canvas.
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15.
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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16.
Write the interval represented on the number line as an inequality.
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17.
Write the interval represented on the number line in interval notation.
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18.
Is this a compound inequality?
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19.
Is this a compound inequality?
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20.
Is this a compound inequality?
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21.
Is this a compound inequality?
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23.
Reasoning: What are the solutions of the inequalities as a compound inequality?
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24.
Reasoning: What are the solutions of the compound in equality in interval notation?
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26.
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'
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27.
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?
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28.
Review Lesson 3-5: Solve the inequality.
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29.
Review Lesson 1-5: Complete each statement with <, =, or >.
  • <
  • =
  • >
  • |3 - 7| __?__ 4
  • |-5| + 2 __?__ 6
  • |6 - 2.5| __?__ 3.3
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30.
Vocabulary Review: Categorize each math sentence as an inequality or an equation.
  • 15 > -12
  • 18 ≤ 35
  • 5x = 15
  • 9 > 3x
  • Inequality
  • Equation
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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
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Use Your Vocabulary: Identify the inequalities that are NOT compound inequalities. Select all that apply.
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33.
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
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34.
Use Your Vocabulary: Which compound inequality from the previous item describes an empty set ?
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35.
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.
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36.
Reflection: Math Success
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