Lesson 8: Practice Problems

Problem 1

Draw a diagram of $x + 3$ and a diagram of $2 x$ when $x$ is 1.
Draw a diagram of $x + 3$ and of $2 x$ when $x$ is 2.
Draw a diagram of $x + 3$ and of $2 x$ when $x$ is 3.
Draw a diagram of $x + 3$ and of $2 x$ when $x$ is 4.
When are $x + 3$ and $2 x$ equal? When are they not equal? Use your diagrams to explain.

Problem 2

Do $4 x$ and $15 + x$ have the same value when $x$ is 5?
Are $4 x$ and $15 + x$ equivalent expressions? Explain your reasoning.

Problem 3

Check that $2 b + b$ and $3 b$ have the same value when $b$ is 1, 2, and 3.
Do $2 b + b$ and $3 b$ have the same value for all values of $b$ ? Explain your reasoning.
Are $2 b + b$ and $3 b$ equivalent expressions?

Problem 4 From Unit 6 Lesson 7

80% of $x$ is equal to 100.

Write an equation that shows the relationship of 80%, $x$ , and 100.
Use your equation to find $x$ .

Problem 5 From Unit 6 Lesson 5

For each story problem, write an equation to represent the problem and then solve the equation. Be sure to explain the meaning of any variables you use.

Jada’s dog was $5 \frac{1}{2}$ inches tall when it was a puppy. Now her dog is $14 \frac{1}{2}$ inches taller than that. How tall is Jada’s dog now?
Lin picked $9 \frac{3}{4}$ pounds of apples, which was 3 times the weight of the apples Andre picked. How many pounds of apples did Andre pick?

Problem 6

Find these products.

$(2.3) \cdot (1.4)$
$(1.72) \cdot (2.6)$
$(18.2) \cdot (0.2)$
$15 \cdot (1.2)$

Problem 7

Calculate $141.75 \div 2.5$ using a method of your choice. Show or explain your reasoning.