# Lesson 6

Modeling with Inequalities

Let's look at solutions to inequalities.

### Problem 1

28 students travel 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 $$12+3n>28$$ or $$12+3n\geq28$$ 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.

### Problem 2

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.
2. 5 barrels catch rainwater in the schoolyard. Four barrels are the same size, and the fifth barrel holds 10 liters of water. Combined, the 5 barrels can hold at least 200 liters of water. Write an inequality whose solution is the possible size of each of the 4 barrels.
3. How are these two problems similar? How are they different?

### Problem 3

Priya looks at the inequality $$12-x>5$$ and says “I subtract a number from 12 and want a result that is bigger than 5. That means that the solutions should be values of $$x$$ that are smaller than something.”

Do you agree with Priya? Explain your reasoning and include solutions to the inequality in your explanation.

### Problem 4

When a store had sold $$\frac25$$ of the shirts that were on display, they brought out another 30 from the stockroom. The store likes to keep at least 150 shirts on display. The manager wrote the inequality $$\frac35x+30 \geq 150$$ to describe the situation.

1. Explain what $$\frac35$$ means in the inequality.
2. Solve the inequality.

3. Explain what the solution means in the situation.

### Problem 5

Select all the inequalities that have the same graph as $$x<4$$.

A:

$$x<2$$

B:

$$x+6<10$$

C:

$$5x<20$$

D:

$$x-2>2$$

E:

$$x<8$$

(From Unit 4, Lesson 3.)