~ 6.13 ~

Reintroducing Inequalities

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Learning Targets

I can explain what the symbols ≥ and ≤ mean.
I can represent an inequality on a number line.
I understand what it means for a number to make an inequality true.

Notes

We use inequalities to describe a range of numbers. In many places, you are allowed to get a driver’s license when you are at least 16 years old. When checking if someone is old enough to get a license, we want to know if their age is at least 16. If h is the age of a person, then we can check if they are allowed to get a driver’s license by checking if their age makes the inequality h > 16 (they are older than 16) or the equation h = 16 (they are 16) true. The symbol ≥ , pronounced “greater than or equal to,” combines these two cases and we can just check if h ≥ 16 (their age is greater than or equal to 16). The inequality h ≥ 16 can be represented on a number line:

Testing solutions to inequalitiesPractice plugging in values to inequalities, like 2x<14, and checking to see if the inequalities hold true.

Activities

13.2 The Roller Coaster

A sign next to a roller coaster at an amusement park 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 x inches tall. Which of the following can be true: x > 60, x = 60, or x < 60? Explain how you know.
Noah’s friend is 2 inches shorter than Noah. Can you tell if Noah’s friend is tall enough to go on the ride? Explain or show your reasoning.
List one possible height for Noah that means that his friend is tall enough to go on the ride, and another that means that his friend is too short for the ride.
On the number line below, show all the possible heights that Noah’s friend could be.
Noah's friend is y inches tall. Use y and any of the symbols <, =, > to express this height.

13.3 Is the Inequality True or False?

The table shows four inequalities and four possible values for x. Decide whether each value makes each inequality true, and complete the table with “true” or “false.” Discuss your thinking with your partner. If you disagree, work to reach an agreement.

Add to Your Notes

Substituting a value in for x, and considering whether the inequality is true is the most direct way to check if the value is a solution!

Summary

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