# Lesson 5 May I Have More, Please? Solidify Understanding

## Jump Start

Determine which inequality matches each phrase.

#### a.

No more than

#### b.

A minimum of

#### c.

More than

#### d.

No less than

#### e.

At least

#### f.

A maximum of

#### g.

Cannot exceed

#### h.

Fewer than

## Learning Focus

Write and solve inequalities to model real situations.

Write solutions to inequalities using set builder and interval notation.

How can inequalities be used to find solutions to real problem situations?

## Open Up the Math: Launch, Explore, Discuss

Elvira, the cafeteria manager, needs to be careful with her spending, and she manages the cafeteria budget so that they can serve the best food at the lowest cost. To do this, Elvira keeps good records and analyzes all her budgets.

### 1.

Elvira’s cafeteria has those cute little cartons of milk that are typical of school lunch. The milk supplier charges

#### a.

Write and solve an inequality that models this situation.

#### b.

Describe in words the quantities that would work in this situation.

#### c.

Write your answer in both interval and set notation.

### 2.

Students love to put ranch dressing on everything, so Elvira needs to keep plenty in stock. The students eat about

#### a.

Write and solve an inequality that models this situation.

#### b.

Describe in words the quantities that would work in this situation.

#### c.

Write your answer in both interval and set notation.

### 3.

The prices on many of the cafeteria foods change during the year. Elvira finds that she has ordered veggie burgers four times and paid

#### a.

Write and solve an inequality that models this situation.

#### b.

Describe in words the quantities that would work in this situation.

#### c.

Write your answer in both interval and set notation.

### 4.

Elvira can purchase ready-made pizzas for

#### a.

Write and solve an inequality that models this situation.

#### b.

Describe in words the quantities that would work in this situation.

#### c.

Write your answer in both interval and set notation.

### 5.

Elvira is comparing prices between two different suppliers of fresh lettuce. Val’s Veggies charges

#### a.

Write and solve an inequality that models this situation.

#### b.

Describe in words the quantities that would work in this situation.

#### c.

Write your answer in both interval and set notation.

### 6.

Each student who buys a school lunch pays

#### a.

Model this situation using an inequality.

#### b.

Describe in words the quantities that would work in this situation.

#### c.

Write your answer in both interval and set notation.

## Ready for More?

River A and River B combine together to form River C. The flow rate of the River C is less than or equal to the sum of the flow rates of the Rivers A and B, but it is greater than or equal to either of the individual flow rates of Rivers A and B. One of the three rivers flows at a rate of

#### a.

Find the minimum flow rate,

#### b.

Find the maximum flow rate,

#### c.

Write an inequality that describes the possible flow rates,

## Takeaways

**Using properties of inequalities to solve inequalities:**

## Adding Notation, Vocabulary, and Conventions

Compound inequality:

Examples:

## Vocabulary

- compound inequality in one variable
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we wrote inequalities to model contexts that had a range of solutions. We used the properties of inequalities to solve the inequalities and found that solving inequalities is very similar to solving equations, but we must be careful when multiplying or dividing by a negative number to reverse the inequality sign. We used interval and set notation to write solutions and learned that many of the solutions that we write are compound inequalities.

### 1.

Graph each equation and find the point where they intersect.

Point of intersection: