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6-8 Grade 7 Unit 6 Lesson 8

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K-5 Math •6-8 Math 9-12 Math

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Grade 6 •Grade 7 Grade 8

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22

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Unit 3
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Unit 6
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Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
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Lesson 17
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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 6, Lesson 8

Reasoning about Solving Equations (Part 2)

Grade 7

Practice

Problem 1

Here is a balanced hanger diagram:

Write an equation to represent the diagram.
Solve the equation by reasoning about the equation or the diagram. Explain your reasoning.

Hanger has 5 groups of a circle + rectangle labeled with 2 on the left, rectangle labeled with 11 on the right

Problem 2

Explain how each part of the equation \(9=3(x+2)\) is represented in the hanger diagram.

\(x\)
9
3
\(x+2\)
\(3(x+2)\)
the equal sign

Balanced hanger, left side, 9 squares each labeled 1. Right side, three groups, each group contains one circle labled x and 2 squares labeled 1.

Problem 3

ForLesson 11: Percentage Contexts

Select the word from the following list that best describes each situation.

You deposit money in a savings account, and every year the amount of money in the account increases by 2.5%.
For every car sold, a car salesman is paid 6% of the car’s price.
Someone who eats at a restaurant pays an extra 20% of the food price. This extra money is kept by the person who served the food.
An antique furniture store pays \$200 for a chair, adds 50% of that amount, and sells the chair for \$300.
The normal price of a mattress is $600, but it is on sale for 10% off.
For any item you purchase in Texas, you pay an additional 6.25% of the item's price to the state government.

Problem 4

ForLesson 3: Reasoning about Equations with Tape Diagrams

Clare drew this diagram to match the equation \(2x+16=50\), but she got the wrong solution as a result of using this diagram.

A tape diagram partitioned into three different sized rectangles, labeled 2, x and 16. The total length of the bar is labeled 50.

What value for \(x\) can be found using the diagram?
Show how to fix Clare’s diagram to correctly match the equation.
Use the new diagram to find a correct value for \(x\).
Explain the mistake Clare made when she drew her diagram.

Tax
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