Lesson 8

Writing and Graphing Inequalities

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.

Solution

For access, consult one of our IM Certified Partners.

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. \(h < 2\)

Solution

For access, consult one of our IM Certified Partners.

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 \(d=\frac12\).

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.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 6, Lesson 14.)

Problem 4

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

Solution

For access, consult one of our IM Certified Partners.

(From 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. \(2x-\frac12\)

Solution

For access, consult one of our IM Certified Partners.

(From Unit 6, Lesson 11.)