Modeling with Inequalities


The stage manager of the school musical is trying to figure out how many sandwiches he can order with the $83 he collected from the cast and crew. Sandwiches cost $5.99 each, so he letsrepresent the number of sandwiches he will order and writes 5.99 83. he solves this to 2 decimal places, getting 13.86.

Activity #1

Graph Inequalities.

  • An inequality is given in each applet below. Move the points on the line so that the line displays the inequality.
  • Use the SOLID OR DASH LINE slider to choose the nature of the line.
  • Use the SHADE LEFT OR RIGHT slider to shade the correct shaded region of the graph.
  • Use the SHOW ANSWER slider to verify your answer.

(1.) x > -1

(2.) x ≤ -2

(3.) y < –1

(4.) y ≥ 0

(5.) y ≤ x

Activity #2

 Write, Solve, and Graph an Inequality.

  • Read the story about the inequality below and answer the questions.

A mover is loading an elevator with many identical 48-pound boxes. The mover weighs 185 pounds. The elevator can carry at most 2000 pounds.

(1.) Write an inequality that says that the mover will not overload the elevator on a particular ride.,

(2.) Solve your inequality and explain what the solution means.

(3.) Graph the solution to your inequality on a number line.

(4.) If the mover asked, “How many boxes can I load on this elevator at a time?” what would you tell them?

Activity #3

 Solve One Variable Inequalities.

Note: You are going to interact with the applet below to find solution sets to inequalities. Enter in an exact boundary value in the input box (i.e. enter “2/6” and not 0.66). Do not simplify your answer.

  • Solve each generated inequality on a separate sheet of paper.
  • Select the appropriate inequality operation on the right side of the applet.
  • Enter the solution set to this inequality in the box. If you enter in the solution set to an inequality correctly, you’ll see a big “CORRECT!!!” sign appear. If you don’t see this sign, click on .

Challenge #1

In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. There are enough tables to fit 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria.

Challenge #2

28 students went on a field trip. They bring a van that can seat 12 students. Elena and Kiran’s teacher asks other adults to drive cars that seat 3 children each to transport the rest of the students. Elena wonders if she should use the inequality  to figure out how many cars are needed. Kiran doesn’t think it matters in this case. Do you agree with Kiran? Explain your reasoning.

Challenge #3

Select all the inequalities that have the same graph as

Quiz Time