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.

Core Lesson

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 ≤ $60

22 + 8x ≤ $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.

Extension Activities

The word problem below is equivalent to22 + 8x ≤ $60.

Tweak the word problem to match the following three inequalities:

(1) 22 + 8x < $60 (2) 15 + 8x ≤ $60 (3) 30 + 4x > $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.

Quick Quiz

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.