Lesson 8

Writing and Graphing Inequalities

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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

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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

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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

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(From Unit 6, Lesson 14.)

Problem 4

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

A:

The number -15 is further away from 0 than the number -12 on the number line.

B:

The number -12 is a distance of 12 units away from 0 on the number line.

C:

The distance between -12 and 0 on the number line is greater than -15.

D:

The numbers 12 and -12 are the same distance away from 0 on the number line.

E:

The number -15 is less than the number -12.

F:

The number 12 is greater than the number -12.

1:

\(|\text-12| > \text-15\)

2:

\(\text-15 < \text-12\)

3:

\(|\text-15| > |\text-12|\)

4:

\(|\text-12| = 12\)

5:

\(12 > \text-12\)

6:

\(|12| = |\text-12|\)

Solution

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(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

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(From Unit 6, Lesson 11.)