Lesson 8: Practice Problems

Problem 1

At the book sale, all books cost less than $5.

What is the most expensive a book could be?
Write an inequality to represent costs of books at the sale.
Draw a number line to represent the inequality.

Problem 2

Kiran started his homework before 7:00 p.m. and finished his homework after 8:00 p.m. Let $h$ represent the number of hours Kiran worked on his homework.

Decide if each statement it is definitely true, definitely not true, or possibly true. Explain your reasoning.

$h > 1$
$h > 2$
$h < 1$
$h < 2$

Problem 3 From Unit 6 Lesson 14

Consider a rectangular prism with length 4 and width and height $d$ .

A rectangular prism with a square base. The width of the base is labeled d and the rectangular face has length 4 and height d.

Find an expression for the volume of the prism in terms of $d$ .
Compute the volume of the prism when $d = 1$ , when $d = 2$ , and when $d = \frac{1}{2}$ .

Problem 4 From Unit 7 Lesson 7

Match the mathematical statements with the statements written in English. All of these statements are true.

$| - 12 | > - 15$
$- 15 < - 12$
$| - 15 | > | - 12 |$
$| - 12 | = 12$
$12 > - 12$
$| 12 | = | - 12 |$

The number -15 is further away from 0 than the number -12 on the number line.
The number -12 is a distance of 12 units away from 0 on the number line.
The distance between -12 and 0 on the number line is greater than -15.
The numbers 12 and -12 are the same distance away from 0 on the number line.
The number -15 is less than the number -12.
The number 12 is greater than the number -12.

Problem 5 From Unit 6 Lesson 11

Here are five sums. Use the distributive property to write each sum as a product with two factors.

$2 a + 7 a$
$5 z - 10$
$c - 2 c^{2}$
$r + r + r + r$
$2 x - \frac{1}{2}$