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Algebra 1 3-7 Complete Lesson: Absolute Value Equations and Inequalities

By Matt Richardson
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Last updated about 2 years ago
33 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! Serena skates toward Darius and then passes by him. She skates at a constant speed of 20 ft/s. At what time(s) is Serena 60 ft from Darius? Select all that apply.
  • 1 second
  • 2 seconds
  • 3 seconds
  • 5 seconds
  • 7 seconds
  • 8 seconds
  • 60 ft from Darius
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Problem 1 Got It? What are the solutions of the equation?
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3.
Problem 1 Got It? Graph and check the solutions.
Include relevant graph detail.
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Problem 2 Got It? Another friend's distnace d from you (in feet) after t seconds is given by d = |80 - 5t|. What does the 5 in the equation represent?
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5.
Problem 2 Got It? Another friend's distnace d from you (in feet) after t seconds is given by d = |80 - 5t|. What does the 80 in the equation represent?
A.SSE.1.b
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6.
Problem 2 Got It? Another friend's distnace d from you (in feet) after t seconds is given by d = |80 - 5t|. At what time is she 60 ft from you?
Select all that apply.
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7.
Problem 3 Got It?
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Problem 4 Got It? What are the solutions of the inequality?
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9.
Problem 4 Got It? Graph the solutions of the inequality.
Include all relevant graph detail.
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Problem 5 Got It? A food manufacturer makes 32-oz boxes of pasta. Not every box weighs exactly 32 oz. The allowable difference from the ideal weight is at most 0.05 oz. Write and solve an absolute value inequality to find the range of allowable weights.
A.SSE.1.b
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11.
Problem 5 Got It? Reasoning: In Problem 5, could you have solved the inequality |w - 213| ≤ 5 by first adding 213 to each side?
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12.
Problem 5 Got It? Reasoning: Explain your response to the previous item.
A.SSE.1.b
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13.
Solve and graph.
Include relevant graph detail.
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14.
Solve and graph.
Include relevant graph detail.
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15.
Solve and graph.
Include relevant graph detail.
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16.
Solve and graph.
Include relevant graph detail.
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17.
Solve and graph.
Include relevant graph detail.
A.SSE.1.b
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18.
Reasoning: How many solutions can you get when you solve absolute value equations? Select all that apply.
A.SSE.1.b
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20.
Compare and Contrast: Explain the similarities and differences in solving the equation |x - 1| = 2 with solving the inequalities |x - 1| ≤ 2 and |x - 1| ≥ 2.
A.SSE.1.b
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21.
Review Lesson 3-6: Write a compound inequality to model the situation. Use the variable E to represent elevation.

The highest elevation in North America is 20,320 ft above sea level at Mount Denali, Alaska. The lowest elevation in North America is 282 ft below sea level at Death Valley, California.
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22.
Review Lesson 1-7: Simplify the expression.
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23.
Review Lesson 1-7: Simplify the expression.
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24.
Review Lesson 1-7: Simplify the expression.
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25.
Review Lesson 1-7: Simplify the expression.
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26.
Review Lesson 3-5: Write the set in set-builder notation.
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27.
Review Lesson 3-5: Write the set in set-builder notation.
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28.
Review Lesson 3-5: Write the set in roster form. C = {n|n is an even number between -15 and -5}

Enter your response in this form: {-2, -1, 0, 1, 2, 3}, with the only spaces following each comma.
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29.
Review Lesson 3-5: Write the set in roster form. D = {k|k is a composite number between 7 and 17}

Enter your response in this form: {-2, -1, 0, 1, 2, 3}, with the only spaces following each comma.
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30.
Vocabulary Review: Mark each statement as True or False.
  • True
  • False
  • To indicate the absolute value of -8, you write |-8|.
  • The absolute value of -8 is -8, since -8 is 8 units from 0 on the number line.
  • The absolute value of -8 is 8, since -8 is 8 units from 0 on the number line.
  • According to the definition of absolute value, if |r|= 3, then r = 3 or r = -3.
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31.
Use Your Vocabulary: Match each expression on the left with its word phrase on the right.
  • m increased by 8
  • m divided by 8
  • m less than 8
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32.
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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33.
Reflection: Math Success
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