Lesson 21: Practice Problems

Problem 1

Noah says that $9 x - 2 x + 4 x$ is equivalent to $3 x$ , because the subtraction sign tells us to subtract everything that comes after $9 x$ .
Elena says that $9 x - 2 x + 4 x$ is equivalent to $11 x$ , because the subtraction only applies to $2 x$ .

Do you agree with either of them? Explain your reasoning.

Problem 2

Identify the error in generating an expression equivalent to $4 + 2 x - \frac{1}{2} (10 - 4 x)$ . Then correct the error.

$4 + 2 x + \frac{- 1}{2} (10 + (- 4 x))$

$4 + 2 x + (- 5) + 2 x$

$4 + 2 x - 5 + 2 x$

$- 1$

Problem 3

Select all expressions that are equivalent to $5 x - 15 - 20 x + 10$ .

$5 x - (15 + 20 x) + 10$
$5 x + (- 15) + (- 20 x) + 10$
$5 (x - 3 - 4 x + 2)$
$- 5 (- x + 3 + 4 x + (- 2))$
$- 15 x - 5$
$- 5 (3 x + 1)$

Problem 4 From Unit 6 Lesson 14

The school marching band has a budget of up to $750 to cover 15 new uniforms and competition fees that total $300. How much can they spend for one uniform?

Write an inequality to represent this situation.
Solve the inequality and describe what it means in the situation.

Problem 5 From Unit 6 Lesson 16

Solve the inequality that represents each story. Then interpret what the solution means in the story.

For every $9 that Elena earns, she gives $x$ dollars to charity. This happens 7 times this month. Elena wants to be sure she keeps at least $42 from this month’s earnings. $7 (9 - x) \geq 42$
Lin buys a candle that is 9 inches tall and burns down $x$ inches per minute. She wants to let the candle burn for 7 minutes until it is less than 6 inches tall. $9 - 7 x < 6$

Problem 6 From Unit 4 Lesson 3

A certain shade of blue paint is made by mixing $1 \frac{1}{2}$ quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 gallons of this shade of blue paint, how much of each color should you mix?