What happens when there is more than one numerical value of x?

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Presentation transcript:

What happens when there is more than one numerical value of x?

In this lesson you will learn to create an inequality given a word problem by using algebraic reasoning.

Let’s Review A variable is a letter or symbol that represents an unknown number or set of numbers. An inequality has more than 1 solution.

A Common Mistake If the value is NOT part of the solution set: If the value IS part of the solution set: > greater than < less than ≥ greater than or equal to ≤ less than or equal to Not using the correct inequality symbol

Core Lesson Write an inequality to represent the following situation: Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8.

To write an inequality from a word problem: 1.What don’t you know? Represent it with a variable! What do you know? 2.Is there more than 1 possible solution? 3.What type of inequality sign is needed?

Core Lesson What don’t we know? How many t-shirts can be bought. Let x = # of t-shirts Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. What do we know? Jeans cost $22. (constant)

Core Lesson Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. Is there more than 1 possible solution? Yes! Because if she bought just 1 t- shirt and the jeans she would have extra money left to buy more t-shirts!

Core Lesson Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. Jeans + Shirts ≤ $60 Jeans + Shirts can’t be more than $60. Jeans + Shirts could equal $60.

Core Lesson Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8. $22 pair of jeans + $8 per t-shirt ≤ $ x ≤ $60

In this lesson you learned to create an inequality given a word problem by using algebraic reasoning.

Guided Practice Write an inequality to represent the situation: Steven had $25 to spend. He spent $10.81, including tax, to buy a new DVD. He needs to save $10 but he wants to buy a snack. If peanuts cost a quarter per package, including tax, what is the maximum number of packages he can buy?

Extension Activities Given a set of inequalities, create equivalent representations in the form of word problems.

The word problem below is equivalent to x ≤ $60. Tweak the word problem to match the following three inequalities: (1) x < $60 (2) x ≤ $60 (3) x > $60 Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t-shirts. Each t-shirt cost $8.

Quick Quiz Devon needs at least 150 points to win a prize. He earned 45 points during round 1 and each time he wins a game in round 2 he will earn 17 points. Write an inequality to represent the amount of x games he will need to win to earn a prize.

Eric is finding money in his coin jar to go to the carnival. He wants to spend no more than $13 there. He brings $8 in bills and some quarters. Write an inequality to represent the amount of quarters he could bring so he spends no more than $13.