# Lesson 8

Writing and Graphing Inequalities

The practice problem answers are available at one of our IM Certified Partners

### Problem 1

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

1. What is the most expensive a book could be?
2. Write an inequality to represent costs of books at the sale.
3. 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.

1. $$h > 1$$

2. $$h > 2$$

3. $$h < 1$$

4. $$h < 2$$

### Problem 3

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

1. Find an expression for the volume of the prism in terms of $$d$$.
2. Compute the volume of the prism when $$d=1$$, when $$d=2$$, and when $$d=\frac12$$.

(From Grade6, Unit 6, Lesson 14.)

### Problem 4

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

(From Grade6, Unit 7, Lesson 7.)

### Problem 5

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

1. $$2a+7a$$
2. $$5z-10$$
3. $$c-2cd$$
4. $$r+r+r+r$$
5. $$2x-\frac12$$
(From Grade6, Unit 6, Lesson 11.)