IM 7.6.8 Lesson: Reasoning about Solving Equations (Part 2)

Select [b]all [/b]the expressions equivalent to [math]2\left(x+3\right)[/math].
Explain why either of these equations could represent this hanger:
[math]14=2\left(x+3\right)[/math] or [math]14=2x+6[/math][br][br][img]data:image/png;base64,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[/img]
Find the weight of one circle. Be prepared to explain your reasoning.
Here is a balanced hanger. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger. Each piece is labeled with its weight.
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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger. Each piece is labeled with its weight.
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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
Here is a balanced hanger. Each piece is labeled with its weight.
[img]data:image/png;base64,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[/img][br]Assign one of these equations to the hanger:
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the diagram.
Explain how to figure out the weight of a piece labeled with a letter by reasoning about the equation.
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Information: IM 7.6.8 Lesson: Reasoning about Solving Equations (Part 2)