Lesson 1
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
- Show that the two triangles are congruent.
- Find the side lengths of \(DEF\) and the angle measures of \(ABC\).
![Two triangles in an x y plane.](https://cms-im.s3.amazonaws.com/dMAZJj8rqoo3ezNig9m6dFgD?response-content-disposition=inline%3B%20filename%3D%228-8.1.C.PP.Image.07b.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.C.PP.Image.07b.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=20240630T202739Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4f54189927b52a3241316da9b9f827d6de5938ef7588085824c8bae3edc271bc)
Solution
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(From Unit 1, Lesson 11.)Problem 4
Here is a polygon on a grid.
![An L shaped figure on a square grid.](https://cms-im.s3.amazonaws.com/4MRdmNAfY9dY3JRsndUDss4W?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.32.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.32.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=20240630T202739Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8e5031d316b233de426efc6993d17ce5de45fc647da68a00d66e39fed7e907a8)
Draw a scaled copy of this polygon that has a perimeter of 30 units. What is the scale factor? Explain how you know.
Solution
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(From Unit 2, Lesson 2.)