Unit 3, Lesson 7

Reasoning about Solving Equations (Part 2)

Accelerated 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 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.

Problem 4

ForLesson 7: Units in Scale Drawings

Lin has a scale model of a modern train. The model is created at a scale of 1 to 48.

The height of the model train is 102 millimeters. What is the actual height of the train in meters? Explain your reasoning.
On the scale model, the distance between the wheels on the left and the wheels on the right is \(1\frac14\) inches. The state of Wyoming has old railroad tracks that are 4.5 feet apart. Can the modern train travel on those tracks? Explain your reasoning.

Problem 5

ForLesson 2: Scale Factors and Making Scaled Copies

Quadrilateral A has side lengths 3, 4, 5, and 6. Quadrilateral B is a scaled copy of Quadrilateral A with a scale factor of 2. Select all of the following that are side lengths of Quadrilateral B.

Problem 6

from an earlier course

Find the value of each variable.

\(a \boldcdot 3 = \text-30\)

\(\text-9\boldcdot b = 45\)

\(\text-89 \boldcdot 12 =c\)

\(d \boldcdot 88 = \text-88,\!000\)

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