Lesson 7
Subtraction in Equivalent Expressions
Problem 1
For each expression, write an equivalent expression that uses only addition.
 \(209+87\)
 \(4x7y5z+6\)
 \(\text3x8y4\frac87z\)
Solution
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Problem 2
Use the distributive property to write an expression that is equivalent to each expression. If you get stuck, consider drawing boxes to help organize your work.
 \(9(4x3y\frac23)\)
 \(\text2(\text6x+3y1)\)
 \(\frac15(20y4x13)\)
 \(8(\textx\frac12)\)
 \(\text8(\textx\frac34y+\frac72)\)
Solution
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Problem 3
Kiran wrote the expression \(x10\) for this number puzzle: “Pick a number, add 2, and multiply by 5.”
Lin thinks Kiran made a mistake.
 How can she convince Kiran he made a mistake?
 What would be a correct expression for this number puzzle?
Solution
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Problem 4
Solve each equation.
 \(5(n4)=\text60\)
 \(\text3t+ \text8=25\)
 \(7p8=\text22\)
 \(\frac25(j+40)=\text4\)
 \(4(w+1)=\text6\)
Solution
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(From Unit 3, Lesson 9.)Problem 5
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.

What is the actual area of the park? Show how you know.

The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure? Show your reasoning.
Solution
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(From Unit 2, Lesson 7.)