The document discusses writing inequalities to represent word problems algebraically. It begins with an overview of variables, inequalities, and common mistakes. An example problem is then presented: writing an inequality for a situation where Debbie has $60 to spend on clothes, buys $22 jeans, and spends the rest on $8 t-shirts. The inequality written is 22 + 8x ≤ 60, where x is the number of t-shirts. Another word problem is then presented as guided practice.

1. Linear Inequality Word
Problems
6-12-2015

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

3. 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.

4. 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

5. 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.

6. 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)

7. 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

8. 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?