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Algebra 1 6-5 Complete Lesson: Linear Inequalities

By Matt Richardson
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Last updated about 2 years ago
22 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! You are buying paperback and hardcover books at a book sale. You can spend at most $20. What are the possible combinations of paperback and hardcover books that you can buy? Explain.
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2.
Problem 1 Got It?
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3.
Problem 1 Got It?
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4.
Problem 2 Got It? What is the graph of the inequality below?
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5.
Problem 3 Got It? What is the graph of the inequality?
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6.
Problem 3 Got It? What is the graph of the inequality?
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Problem 4 Got It? For a party, you can spend no more than $12 on nuts. Peanuts cost $2/lb. Cashews cost $4/lb. What are three possible combinations of peanuts and cashews you can buy. Graph the inequality.
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8.
Problem 5 Got It?
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9.
Is (-1, 4) a solution of the inequality? Explain.
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10.
Graph the linear inequality on the canvas below by hand, without the aid of a graphing utility.
After that, graph the inequality on the embedded Desmos graphing calculator above.
Edit your graph, as needed.
As always, include important graph detail: label the axes, indicate axis scale by labeling at least one value on each axis, add arrows to the ends of lines, ensure that your line is appropriately dashed or solid, and shade one side of the boundary line, as appropriate.
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11.
Graph the linear inequality. Zoom and pan your graph to establish an appropriate viewing window.
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12.
What is an inequality that represents the graph shown?
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13.
Vocabulary: How is a linear inequality in two variables like a linear equation in two variables? How are they different?
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14.
Writing: To graph the inequality below, do you shade above or below the boundary line? Explain.
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15.
Reasoning: Write an inequality that describes the region of the coordinate plane not included in the graph of the inequality below.
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16.
Review Lesson 6-4: An electrician spends $12,000 on initial costs to start a new business. He estimates his expenses at $25 per day. He expects to earn $150 per day. If his estimates are correct, after how many working days will he break even? Enter only a number.
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17.
Review Lesson 3-6: What compound inequality represents the phrase "all real numbers that are greater than 2 and less than or equal to 7"?
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18.
Review Lesson 6-1: Solve the system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.
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19.
Vocabulary Review A solution is a value or values which, when substituted for a variable, make an equation true. Determine the solution of each inequality below.
  • Solution: x > 20
  • Solution: x < 20
  • Solution: m > 6
  • Solution: m < 6
  • x + 17 < 37
  • 2m + 3 > 15
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20.
Use Your Vocabulary: Identify the linear inequality in two variables.
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21.
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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22.
Reflection: Math Success
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