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Algebra 1 3-3 Complete Lesson: Solving Inequalities Using Multiplication or Division

By Matt Richardson
Last updated almost 3 years ago
21 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! Drag the appropriate inequality sign to fill in each blank.

  • <
  • >
  • (4)(3) ___ (1)(3)
  • (4)(2) ___ (1)(2)
  • (4)(1) ___ (1)(1)

Solve It! Drag the appropriate inequality sign to fill in each blank.

  • <
  • >
  • (4)(-1) ___ (1)(-1)
  • (4)(-2) ___ (1)(-2)
  • (4)(-3) ___ (1)(-3)

Solve It! Consider the previous item. What happens to the inequality symbol when you multiply each side of an expression by a positive number? A negative number? Justify your reasoning.

Problem 1 Got It? What are the solutions of the inequality?

Problem 1 Got It? Graph the solutions of the inequality.
Include all relevant graph detail.

Problem 2 Got It? What are the solutions of the inequality?

Problem 2 Got It? Graph the solutions of the inequality.
Include all relevant graph detail.

Problem 3 Got It? A student club plans to buy food for a soup kitchen. A case of vegetables costs $10.68. The club can spend at most $50 for this project. What are the possible numbers of cases the club can buy? Categorize the number of cases.

  • 1 case
  • 2 cases
  • 3 cases
  • 4 cases
  • 5 cases
  • 6 cases
  • 7 cases
  • The club can afford:
  • The club can not afford:

Problem 3 Got It? Reasoning: In Problem 3, why do you round to the greater whole number?

Problem 4 Got It? What are the solutions of the inequality?

Problem 4 Got It? Graph the solutions of the inequality.
Include all relevant graph detail.

Match each inequality with its graph.

  • x + 2 > -1
  • -x/3 < -1
  • x - 4 ≤ -1
  • -3x ≥ 9
  • Graph A
  • Graph B
  • Graph C
  • Graph D

Which operation would you use to solve each inequality on the right? Explain.

  • Addition; This inverse operation will isolate the variable in the inequality.
  • Subtraction; This inverse operation will isolate the variable in the inequality.
  • Multiplication; This inverse operation will isolate the variable in the inequality.
  • Division; This inverse operation will isolate the variable in the inequality.

Error Analysis: Describe and correct the error in the solution.

Review Lesson 2-3: Solve the equation.
Enter only a number.

Review Lesson 2-3: Solve the equation.
Enter only a number.

Review Lesson 2-3: Solve the equation.
Enter only a number.

Vocabulary Review: Drag the inequalities into the Inequality category.

  • 5 + x < 6
  • 7 - y ≥ 2
  • a + b = 12
  • m - 3 > 5
  • 2 + 3 = 3 + 2
  • Inequality

Vocabulary Review: Match each inequality on the left with its equivalent inequality on the right.

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.

Reflection: Math Success