# Lesson 9: Solutions of Inequalities

Let’s think about the solutions to inequalities.

## 9.1: Unknowns on a Number Line

The number line shows several points, each labeled with a letter.

1. Fill in each blank with a letter so that the inequality statements are true.

a. _______ > _______

b. _______ < _______

2. Jada says that she found three different ways to complete the first question correctly. Do you think this is possible? Explain your reasoning.
3. List a possible value for each letter on the number line based on its location.

## 9.2: Amusement Park Rides

Priya finds these height requirements for some of the rides at an amusement park.

to ride the . . .  you must be . . .
row 1 High Bounce between 55 and 72 inches tall
row 2 Climb-A-Thon under 60 inches tall
row 3 Twirl-O-Coaster 58 inches minimum
1. Write an inequality for each of the the three height requirements. Use $h$ for the unknown height. Then, represent each height requirement on a number line.

High Bounce

Climb-A-Thon

Twirl-O-Coaster

2. Han’s cousin is 55 inches tall. Han doesn’t think she is tall enough to ride the High Bounce, but Kiran believes that she is tall enough. Do you agree with Han or Kiran? Be prepared to explain your reasoning.
3. Priya can ride the Climb-A-Thon, but she cannot ride the High Bounce or the Twirl-O-Coaster. Which, if any, of the following could be Priya’s height? Be prepared to explain your reasoning.

59 inches

53 inches

56 inches

4. Jada is 56 inches tall. Which rides can she go on?
5. Kiran is 60 inches tall. Which rides can he go on?
6. The inequalities $h < 75$ and $h > 64$ represent the height restrictions, in inches, of another ride. Write three values that are solutions to both of these inequalities.

## 9.3: What Number Am I?

Your teacher will give your group two sets of cards—one set shows inequalities and the other shows numbers. Arrange the inequality cards face up where everyone can see them. Stack the number cards face down and shuffle them.

To play:

• Nominate one member of your group to be the detective. The other three players are clue givers.

• One clue giver picks a number from the stack and shows it only to the other clue givers. Each clue giver then chooses an inequality that will help the detective identify the unknown number.

• The detective studies the inequalities and makes three guesses.

• If the detective cannot guess the number correctly, the clue givers must choose an additional inequality to help. Add as many inequalities as needed to help the detective identify the correct number.

• When the detective succeeds, a different group member becomes the detective and everyone else is a clue giver.

• Repeat the game until everyone has had a turn playing the detective.