Unit 6

Different Options for Solving One Equation

Expressions, Equations, and Inequalities

Lesson 10

Expressions and Equations

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Let’s think about which way is easier when we solve equations with parentheses.

Unit 6 ● Lesson 10

Learning

Goal

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Solve Each Equation

Unit 6 ● Lesson 10 ● Activity 1

100(x – 3) = 1,000

500(x – 3) = 5,000

0.03(x – 3) = 0.3

0.72(x + 2) = 7.2

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Warm-up: Algebra Talk

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Analyzing Solution Methods

Unit 6 ● Lesson 10 ● Activity 2

Three students each attempted to solve the equation , but got different solutions. Here are their methods. Do you agree with any of their methods, and why?

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Noah’s method:

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Analyzing Solution Methods

Unit 6 ● Lesson 10 ● Activity 2

Elena’s method:

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Andre’s method:

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Solution Pathways

Unit 6 ● Lesson 10 ● Activity 3

3(x + 2) = 21

• What might the hanger diagram look like for this equation?
• What choices can you make to find the solution? Which choice might be easier?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Solution Pathways

Unit 6 ● Lesson 10 ● Activity 3

For each equation, try to solve the equation using each method (dividing each side first, or applying the distributive property first). Some equations are easier to solve by one method than the other. When that is the case, stop doing the harder method and write down the reason you stopped.

• 2,000(x – 0.03) = 6,000
• 2(x + 1.25) = 3.5
• -10(x – 1.7) = -3
• 5.4 = 0.3(x + 8)

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Solution Pathways

Unit 6 ● Lesson 10 ● Activity 3

• The solution to each equation is shown.
• For each equation, which solution method was easiest for you: to divide first or to distribute first? Explain your reasoning.
• 2,000(x – 0.03) = 6,000

x = 3.03

• 2(x + 1.25) = 3.5

x = 0.5

x =

• -10(x – 1.7) = -3

x = 2

• 5.4 = 0.3(x + 8)

x = 10

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Different Options for Solving One Equation

Unit 6 ● Lesson 10

• What are the two main ways we can approach solving equations like the ones we saw today?
• What kinds of things do we look for to decide which approach is better?
• How can we check if our answer is a solution to the original equation?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 6 ● Lesson 10

• For an equation like 3(x + 2) = 15, I can solve it in two different ways: by first dividing each side by 3, or by first rewriting 3(x + 2) using the distributive property.
• For equations with more than one way to solve, I can choose the easier way depending on the numbers in the equation.

Learning

Targets

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Solve Two Equations

Unit 6 ● Lesson 10 ● Activity 4

Solve each equation. Show or explain your method.

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• 8.88 = 4.44(x – 7)

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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