Algebra 2 1-5 Complete Lesson: Solving Inequalities

By Matt Richardson

Last updated about 3 years ago

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 want to download some new songs on your MP3 player. Each song will use about 4.3 MB of space. The amount of space available on your MP3 player is shown in the image. At most, how many songs can you download? Hint: 1 GB = 1000 MB

Enter only a whole number without a comma.

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Problem 1 Got It?

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Problem 2 Got It? What is the solution of the inequality?

A.CED.1

Problem 2 Got It? Graph the solution from the previous item on the canvas.
Include relevant details, label points of interest and establish scale.

A.CED.1

Problem 3 Got It?

A.CED.1

Problem 4 Got It?

Problem 5 Got It? What is the solution of the inequality? Graph the solution on the canvas.
Include relevant details, label points of interest and establish scale.

A.CED.1

Problem 5 Got It? Reasoning: Is the compound inequality in Problem 5 always, sometimes, or never true?

Problem 6 Got It? What is the solution of the inequality? Graph the solution on the canvas.
Include relevant details, label points of interest and establish scale.

A.CED.1

Problem 6 Got It? What is the solution of the inequality? Graph the solution on the canvas.
Include relevant details, label points of interest and establish scale.

A.CED.1

Write an inequality that represents the sentence. Rachel's hair is at least as long as Julia's.

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Write an inequality that represents the sentence. The wind speeds of tropical storms are at least 40 mi/h, but less than 74 mi/h.

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Solve the inequality. Graph the solution. Include relevant graph detail.

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Solve the inequality. Graph the solution. Include relevant graph detail.

A.CED.1

Solve the inequality. Graph the solution. Include relevant graph detail.

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Reasoning: Make up an example to help explain why you must reverse the inequality symbol when you multiply or divide by a negative number.

Compare and Contrast: Describe how the properties of inequality are similar to the properties of equality and how they differ.

Provide an Example: Write an inequality for which the solution is the set of all real numbers.

Error Analysis: Your classmate says that you cannot write a compound inequality that has no solution. Do you agree? If so, explain why. If not, give a counterexample.

Review Lesson 1-3: Simplify the expression.

Review Lesson 1-4: Match each equation with its solution. Check your answers.

no solution
-20
4

Vocabulary Review: Classify each item in the left column as an equation or as an inequality.

15 > 32x
-27 ≠ 3x
45 < 46
17x = 34

Equation
Inequality

Use Your Vocabulary: A student uses the word compound in three different sentences. The sentences are listed in the right column. Tag sentences that correctly use the word with a √ symbol. Tag sentences that do not with a ⊗ symbol.

In chemistry class we learned about various chemical compounds.
Compound inequalities contain more than one inequality symbol.
To simplify an expression, compound like terms.

Use Your Vocabulary: Match the appropriate inequality symbol with each phrase on the right.

x is at most 25
x is not equal to 25
x is greater than 25
x is at least 25

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.

Algebra 2 1-5 Complete Lesson: Solving Inequalities

Solve It! You want to download some new songs on your MP3 player. Each song will use about 4.3 MB of space. The amount of space available on your MP3 player is shown in the image. At most, how many songs can you download? Hint: 1 GB = 1000 MBEnter only a whole number without a comma.

Problem 1 Got It?

Problem 2 Got It? What is the solution of the inequality?

Problem 2 Got It? Graph the solution from the previous item on the canvas. Include relevant details, label points of interest and establish scale.

Problem 3 Got It?

Problem 4 Got It?

Problem 5 Got It? What is the solution of the inequality? Graph the solution on the canvas. Include relevant details, label points of interest and establish scale.

Problem 5 Got It? Reasoning: Is the compound inequality in Problem 5 always, sometimes, or never true?

Problem 6 Got It? What is the solution of the inequality? Graph the solution on the canvas. Include relevant details, label points of interest and establish scale.

Problem 6 Got It? What is the solution of the inequality? Graph the solution on the canvas. Include relevant details, label points of interest and establish scale.

Write an inequality that represents the sentence. Rachel's hair is at least as long as Julia's.

Write an inequality that represents the sentence. The wind speeds of tropical storms are at least 40 mi/h, but less than 74 mi/h.

Solve the inequality. Graph the solution. Include relevant graph detail.

Solve the inequality. Graph the solution. Include relevant graph detail.

Solve the inequality. Graph the solution. Include relevant graph detail.

Reasoning: Make up an example to help explain why you must reverse the inequality symbol when you multiply or divide by a negative number.

Compare and Contrast: Describe how the properties of inequality are similar to the properties of equality and how they differ.

Provide an Example: Write an inequality for which the solution is the set of all real numbers.

Error Analysis: Your classmate says that you cannot write a compound inequality that has no solution. Do you agree? If so, explain why. If not, give a counterexample.

Review Lesson 1-3: Simplify the expression.

Review Lesson 1-3: Simplify the expression.

Review Lesson 1-3: Simplify the expression.

Review Lesson 1-4: Match each equation with its solution. Check your answers.

Vocabulary Review: Classify each item in the left column as an equation or as an inequality.

Use Your Vocabulary: A student uses the word compound in three different sentences. The sentences are listed in the right column. Tag sentences that correctly use the word with a √ symbol. Tag sentences that do not with a ⊗ symbol.

Use Your Vocabulary: Match the appropriate inequality symbol with each phrase 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

Solve It! You want to download some new songs on your MP3 player. Each song will use about 4.3 MB of space. The amount of space available on your MP3 player is shown in the image. At most, how many songs can you download? Hint: 1 GB = 1000 MB

Enter only a whole number without a comma.

Problem 2 Got It? Graph the solution from the previous item on the canvas.
Include relevant details, label points of interest and establish scale.

Problem 5 Got It? What is the solution of the inequality? Graph the solution on the canvas.
Include relevant details, label points of interest and establish scale.

Problem 6 Got It? What is the solution of the inequality? Graph the solution on the canvas.
Include relevant details, label points of interest and establish scale.

Problem 6 Got It? What is the solution of the inequality? Graph the solution on the canvas.
Include relevant details, label points of interest and establish scale.

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.