# Graphing Solutions to Inequalities

Video solutions to help Grade 7 students learn how to graph solutions to inequalities taking care to interpret the solutions in the context of the problem.

## New York State Common Core Math Module 3, Grade 7, Lesson 15

### Lesson 15 Student Outcomes

• Students graph solutions to inequalities taking care to interpret the solutions in the context of the problem.

Classwork

Exercise 1
1. Two identical cars need to fit into a small garage. The opening is 23 feet 6 inches wide, and there must be at least 3 feet 6 inches of clearance between the cars and between the edges of the garage. How wide can the cars be?

Example 1
A local car dealership is trying to sell all of the cars that are on the lot. Currently, it has 525 cars on the lot, and the general manager estimates that they will consistently sell 50 cars per week. Estimate how many weeks it will take for the number of cars on the lot to be less than 75.
Write an inequality that can be used to find the number of w full weeks. Since w is the number of full or complete weeks, when w = 1 means at the end of week 1.
Solve and graph the inequality.
Verify the solution.

Exercise 2
2. The cost of renting a car is \$25 per day plus a one time fee of \$75.50 for insurance. How many days can the car be rented if the total cost is to be no more than \$525?
a. Write an inequality to model the situation.
b. Solve and graph the inequality.
c. Interpret the solution in the context of the problem.