Algebra 1 Lesson 2.4 Complete Lesson: Solving Multi-Step Inequalities

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

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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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Review Lesson 3-3: Solve the inequality.

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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

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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 ?.

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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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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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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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Notes: Take a clear picture or screenshot of your notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

10

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?

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

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.

Problem 5 Got It?

Problem 5 Got It?

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

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 ≥ ?

Review Lesson 3-3: Solve the inequality.

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

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 __?__.

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

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

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

Notes: Take a clear picture or screenshot of your notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

Reflection: Math Success

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 ?.