Unit 3, Lesson 13
Solutions of Inequalities
Accelerated 7
13.1
Warm-up
Andre drew this number line to represent .
Do you agree with Andre’s number line? Explain your reasoning.
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Andre drew this number line to represent .
Do you agree with Andre’s number line? Explain your reasoning.
Priya finds these height requirements for some of the rides at an amusement park.
| To ride the . . . | you must be . . . |
|---|---|
| High Bounce | between 55 and 72 inches tall |
| Climb-A-Thon | under 60 inches tall |
| Twirl-O-Coaster | 58 inches minimum |
Write equations and/or inequalities for the height requirements of each ride. Use for the unknown height. Then, represent each height requirement on a number line.
High Bounce
Climb-A-Thon
Twirl-O-Coaster
Priya can ride the Climb-A-Thon, but she cannot ride the High Bounce or the Twirl-O-Coaster. Which of the following could be Priya’s height? Be prepared to explain your reasoning.
Jada is 56 inches tall. Which rides can she go on?
Kiran is 60 inches tall. Which rides can he go on?
The inequalities and represent the height restrictions, in inches, of another ride. Write three values that are solutions to both of these inequalities.
A sign next to a roller coaster says, “You must be at least 60 inches tall to ride.” Noah is happy to know that he is tall enough to ride.
Noah is inches tall. Which of the following can be true? Explain how you know.
On the number line, show all the possible heights that Noah’s friend could be.
Inequalities can be used to describe a range of numbers. Let’s say a movie ticket costs less than \$15. If represents the cost of a movie ticket, we can use to express what we know about the cost of a ticket.
Any value of that makes the inequality true is called a solution to the inequality.
For example, 5 is a solution to the inequality because (or “5 is less than 15”) is a true statement, but 17 is not a solution because (“17 is less than 15”) is not a true statement.
The inequality can be represented on a number line. The open circle at 15 shows that 15 is not a solution. The shading and arrow pointing left from 15 shows that all numbers less than 15 are solutions.
Here’s another example. In many places, people are eligible to get a driver’s license when they are at least 16 years old. If is the age of a person, then we can check if they are eligible to get a driver’s license by checking if their age makes the inequality (they are older than 16) or the equation (they are 16) true. The symbol , pronounced “greater than or equal to,” combines these two cases and we can just check if (their age is greater than or equal to 16).
The inequality can be represented on a number line. The closed, or filled in, circle at 16 shows that 16 is a solution. The shading and arrow pointing right from 16 shows that all numbers greater than 16 are also solutions.
A solution to an inequality is a number that can be used in place of the variable to make the inequality true.