Lesson 7: Practice Problems

Problem 1

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

$20 - 9 + 8 - 7$
$4 x - 7 y - 5 z + 6$
$- 3 x - 8 y - 4 - \frac{8}{7} z$

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.

$9 (4 x - 3 y - \frac{2}{3})$
$- 2 (- 6 x + 3 y - 1)$
$\frac{1}{5} (20 y - 4 x - 13)$
$8 (- x - \frac{1}{2})$
$- 8 (- x - \frac{3}{4} y + \frac{7}{2})$

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.

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

Problem 4 From Unit 3 Lesson 9

Solve each equation.

$5 (n - 4) = - 60$
$- 3 t + (- 8) = 25$
$7 p - 8 = - 22$
$\frac{2}{5} (j + 40) = - 4$
$4 (w + 1) = - 6$

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.