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Algebra 2 2-8 Complete Lesson: Two-Variable Inequalities

Last updated almost 4 years ago
26 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.
Solve It! You have a gift card for a store that sells used CDs and paperback books.
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How many of each type of item can you afford? Categorize each purchasing scenario.

  • 9 CDs
  • 16 books
  • 6 CDs and 6 books
  • 6 CDs and 9 books
  • 2 CDs and 13 books
  • Can afford
  • Can NOT afford
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Suppose you want to use as much of the gift card as possible. Which purchasing option leaves the smallest balance on the gift card?

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Problem 1 Got It? What is the graph of the inequality? Graph the inequality on the canvas using colors other than black. Include all relevant graph detail.

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Problem 1 Got It? What is the graph of the inequality? Graph the inequality on the canvas using colors other than black. Include all relevant graph detail.

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Problem 2 Got It? Suppose that you decide to spend no more than $30 for tickets. Graph an inequality to represent all possible combinations of ticket types. Construct your graph on the canvas using colors other than black. Include relevant graph detail and establish the scale of the axes.

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Problem 2 Got It? Reasoning: Why does the graph in the previous item only include Quadrant I?

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Problem 3 Got It? What is the graph of the absolute value inequality? Graph the inequality on the canvas using colors other than black. Include all relevant graph detail.

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Problem 3 Got It? Graph the absolute value inequality. Zoom and pan your graph to leave an appropriate scale and viewing window.

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Problem 4 Got It?

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Problem 4 Got It?

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Graphing: What is the graph of the inequality? Graph the inequality on the canvas using colors other than black. Include all relevant graph detail.

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Graphing: What is the graph of the inequality? Graph the inequality on the canvas using colors other than black. Include all relevant graph detail.

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Graphing: What is the graph of the absolute value inequality? Graph the inequality on the canvas using colors other than black. Include all relevant graph detail.

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Graphing: Graph the absolute value inequality. Zoom and pan your graph to leave an appropriate scale and viewing window.

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Reasoning: Is the ordered pair a solution of the inequality? Explain.

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Review Lesson 2-7: Graph the absolute value function by translating the graph of its parent function. Use a color other than black.

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Review Lesson 2-2: Tag each equation based on whether y varies directly with x. If it does, also tag it with its constant of variation.

  • y varies directly with x
  • y does NOT vary directly with x
  • constant of variation: -5
  • constant of variation: 3
  • constant of variation: 100
  • y = x + 3
  • y = 100x
  • -5 = y + x
  • 5x + y = 0
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Graphing: Make a scatter plot of the data. Consider the correlation between variables. Zoom and pan your scatter plot to establish an appropriate viewing window.

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Describe the correlation between the variables in the previous item.

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Vocabulary Review: Identify each statement based on whether or not it is an inequality.

  • 15 < 32
  • -27 ≠ 3x
  • 17x = 34
  • 46 > 45
  • Inequality
  • NOT an inequality
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Vocabulary Review: Complete each inequality with an inequality symbol from the left.

  • <
  • >
  • -2 __?__ 1
  • 0.05 __?__ 0.5
  • 8/6 __?__ 16/6
  • |-3.5| __?__ -4
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Use Your Vocabulary: Categorize each inequality based on the boundary line of its graph.

  • y < 3x
  • 2y - 3x ≤ 9
  • 4y ≥ x - 1
  • y > -5x + 4
  • Solid boundary line
  • Dashed boundary line
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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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Reflection: Math Success