Lesson 7

For each expression, write an equivalent expression that uses only addition.

1. \(20-9+8-7\)
2. \(4x-7y-5z+6\)
3. \(\text-3x-8y-4-\frac87z\)

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.

1. \(9(4x-3y-\frac23)\)
2. \(\text-2(\text-6x+3y-1)\)
3. \(\frac15(20y-4x-13)\)
4. \(8(\text-x-\frac12)\)
5. \(\text-8(\text-x-\frac34y+\frac72)\)

Kiran wrote the expression \(x-10\) for this number puzzle: “Pick a number, add -2, and multiply by 5.”

Lin thinks Kiran made a mistake.

1. How can she convince Kiran he made a mistake?
2. What would be a correct expression for this number puzzle?

Solve each equation.

1. \(5(n-4)=\text-60\)
2. \(\text-3t+ \text-8=25\)
3. \(7p-8=\text-22\)
4. \(\frac25(j+40)=\text-4\)
5. \(4(w+1)=\text-6\)

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.

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

2. 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.