Lesson 8
Writing and Graphing Inequalities
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.
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.
-
\(h > 1\)
-
\(h > 2\)
-
\(h < 1\)
-
\(h < 2\)
Solution
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Problem 3
Consider a rectangular prism with length 4 and width 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 \(d=\frac12\).
![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.](https://cms-im.s3.amazonaws.com/RX9RiDGR98kHCkwun3crGML2?response-content-disposition=inline%3B%20filename%3D%226-6.6.A.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%276-6.6.A.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182329Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2928dcc1ebacd0a793fbed1084d6f018eae871bb27914890cbce888db083cf19)
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.
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.
- \(2a+7a\)
- \(5z-10\)
- \(c-2cd\)
- \(r+r+r+r\)
- \(2x-\frac12\)
Solution
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(From Unit 6, Lesson 11.)