Write and graph inequalities for real-world conditions. (Part 2)
Lessons 9 and 10 engage students in using inequalities to represent constraints in real-world situations. In Lesson 10, students interpret inequalities for different situations and distinguish between a continuous solution and a discrete solution.
The variable $$w$$ represents the number of words in Erica’s English essay.
Erica’s teacher assigned another essay for homework. She gave the students a minimum number of words and a maximum number of words to include in their essays. The number of words in ten students’ essays are shown below. All students stayed within the boundaries given by their teacher.
133 115 196 210 154 102 246 250 218 179
Frank wrote the inequality $$x>100$$ to represent the number of words to include in the essay.
Hayat wrote the inequality $$x\leq250$$ to represent the number of words to include in the essay.
Do you agree with the inequalities written by Frank and Hayat? Explain why or why not.
Two similar situations are described below.
Situation A: A backpack can hold at most 8 books.
Situation B: A backpack can hold at most 8 pounds.
Draw a graph for each situation to represent the solution set. Compare and contrast the two graphs.
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
The variable $$s$$ represents Phil’s driving speed in miles per hour on a highway.
On a different road, Phil noticed the speed limit and checked his speed several times to make sure he was driving within the limit. These were his speeds when he checked:
48 45 47 44
If Phil was driving within the speed limit, which inequality could represent the speed limit of the road that Phil was driving on?