Lesson 12
Balanced Moves
Problem 1
In this hanger, the weight of the triangle is \(x\) and the weight of the square is \(y\).

Write an equation using \(x\) and \(y\) to represent the hanger.

If \(x\) is 6, what is \(y\)?
Solution
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Problem 2
Andre and Diego were each trying to solve \(2x+6=3x8\). Describe the first step they each make to the equation.
 The result of Andre’s first step was \(\textx+6=\text8\).
 The result of Diego’s first step was \(6=x8\).
Solution
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Problem 3
Match each set of equations with the move that turned the first equation into the second.
Solution
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Problem 4
What is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning.
Solution
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Problem 5
Here is a balanced hanger diagram.
Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and \(x\) represents the weight of each square. Select all equations that represent the hanger.
\(x+x+x+x+11=x+11.5\)
\(2x=0.5\)
\(4x+5+6=2x+2.5+6\)
\(2x+2.5=3\)
\(4x+2.5+2.5+3+3=2x+2.5+3+3+3\)
Solution
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