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Algebra 1 3-4 Complete Lesson: Solving Multi-Step Inequalities

By Matt Richardson
Last updated over 2 years ago
25 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.
1.

Solve It! Math Club members are selling Pi Day T-shirts for $7.50 each. The goal is to raise $500 by Friday. The figure shows how much they have raised by Wednesday. What is the minimum number of shirts they must still sell in order to reach their goal?

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 3 Got It?

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Problem 4 Got It? Reasoning: The first step in solving Problem 4 was to subtract 3n from each side of the inequality. What else could have been the first step in solving the inequality? Explain.

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Problem 5 Got It?

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Problem 5 Got It?

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16.

Reasoning: Can you solve the inequality 2(x - 3) ≤ 10 without using the Distributive Property? Explain.

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17.

Error Analysis: Your friend says that the solutions of the inequality -2(3 - x) > 2x - 6 are all real numbers. Do you agree with your friend? Explain. What if the inequality symbol was ≥ ?

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18.

Review Lesson 3-3: Solve the inequality.

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19.

Review Lesson 1-3: Match each number set into its number family.

  • the nonnegative integers
  • the counting numbers
  • ..., -3, -2, -1, 0, 1, 2, 3, ...
  • Natural Numbers
  • Whole Numbers
  • Integers
20.

Vocabulary Review: Fill in the blank: You must reverse the direction of the inequality symbol when you multiply both sides of an inequality by a number that is __?__.

21.

Vocabulary Review: Decide if the inequality symbol will change when you solve each inequality. Categorize the inequalities appropriately.

  • 3t < 6
  • -8s < 4
  • 5x ≤ -10
  • -4 ≤ -2a
  • Reverse
  • Stay the same
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22.

Use Your Vocabulary: Use the words at least or at most to complete each sentence.

  • at least
  • at most
  • You must be __?__ 18 years of age to vote in a national election.
  • An elevator can safely carry __?__ 15 people.
  • When water boils, you know the temperature is __?__ 212°F.
  • If all books cost $3 and Jane has $20, she can buy __?__ books.
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23.

Use Your Vocabulary: Now match the appropriate inequality symbol with each sentence.

  • ≥
  • ≤
  • You must be __?__ 18 years of age to vote in a national election.
  • An elevator can safely carry __?__ 15 people.
  • When water boils, you know the temperature is __?__ 212°F.
  • If all books cost $3 and Jane has $20, she can buy __?__ books.
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24.

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.

25.

Reflection: Math Success

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