Lesson 7

Subtraction in Equivalent Expressions

Problem 1

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

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

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.

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

Problem 3

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?

Problem 4

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. $$4(w+1)=\text-6$$

Solution

(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.

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.