Lesson 1
Writing and Graphing Inequalities
Let’s write 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.
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.
-
\(h > 1\)
-
\(h > 2\)
-
\(h < 1\)
-
\(h < 2\)
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033509Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0cdc7490a7860101fb210dadceb043e82d26531de919ba8acb33db3605d92dae)
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%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033509Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=097621379f27e4bd00e4b82b217022952fdbb15aea661204254eca22279b67b4)
Draw a scaled copy of this polygon that has a perimeter of 30 units. What is the scale factor? Explain how you know.