The document contains notes from an algebra lesson that covers solving one-step inequalities using addition, subtraction, multiplication, and division. It includes examples of writing verbal phrases to describe inequalities and graphing inequality solutions on a number line. Key points covered are the properties of inequalities when multiplying or dividing by negative numbers, which causes the direction of the inequality symbol to flip. Students are provided practice solving and graphing various one-step inequalities.

1. Today:
∞ Warm Up
∞ Khan Academy Practice
∞ Solving One-Step Inequalities
∞ Using Addition, Subtraction,
Multiplication & Division
∞ Class Work
December 1, 2015

3. Determine the inequality represented on the graph
x < -4

4. The product of two numbers is 30. One of the numbers is
x. What is the other number?
We have discussed how algebra is really a set of rules, or
truths about the behavior of numbers.
Where arithmetic states that 5•6 = 30, algebra represents
the larger patterns and relationships of numbers such as:
Write the pattern, or relationship for the following:
Two consecutive numbers
consecutive odd/even numbers
A number and its opposite A number and its reciprocal
The sum of two numbers is 35. One of the numbers is x.
What is the other number?

5. The difference of two numbers is 45, and the smaller
number is x. What is the other number?
The difference of two numbers is 45, and the larger
number is n. What is the other number?
The larger of two consecutive even numbers is x. What is
the other number?
Donna is x years old. Her mother is three years more
than twice as old. How old is Donna’s mother?
Donna is 16 years old. How old is Donna’s mother?
Donna’s now 42. Her mother is...
Write the pattern, or relationship for the following:
Mike has c cents, which are all dimes. How many
dimes does he have?

6. Solving One-Step Inequalities
Using Addition, Subtraction,
Multiplication & Division
Goal
To solve and graph one-step inequalities in one
variable using addition or subtraction.

7. EXAMPLE 1 Graph an Inequality in One Variable
Write a verbal phrase to describe the inequality.
Then graph the inequality.
INEQUALITY VERBAL PHRASE GRAPH
1. x < 2
All real numbers
greater than -2
2.
Use your notebook for both the phrase and the graph.

8. Write a verbal phrase to describe the inequality. Then
graph the inequality.
Graph an Inequality in One Variable.
x  -1

9. A solution of an inequality in one variable is a value of
the variable that makes the inequality true.
Equivalent inequalities have the same solutions.
EXAMPLE: x  5 and 5  x are equivalent inequalities.

10. Solve the inequality. Then graph the solution.
Use Subtraction to Solve an Inequality
5. x + 4 < 7
-3 < y – 2

11. 11. Ms. Dewey is flying to San Diego to see her parents. The
airline lets her check up to 65 pounds of luggage for free. Her
suitcase weighs 37 pounds. How much can her other suitcase
weigh without paying a penalty?
Write and Graph an Inequality in One Variable
We don’t know the weight of
the second suitcase, w.
37 + w < 65
-37 -37
w < 28 lb
The 2nd suitcase has to be no more
than 28 pounds.

12. Solve the inequality. Then graph the solution
Multiply or Divide by a Positive Number.
4. -21  3y
1.
2
1
4

k

13. Things to remember about Multiplying and Dividing
Inequalities!
• Divide both sides of an inequality by a NEGATIVE number
and the inequality flips and faces the other way.
• Multiply both sides of an inequality by a NEGATIVE
number and the inequality flips and faces the other way.

14. EXAMPLE 2 Multiply by a Negative Number
Solve . Then graph the solution.5
2
1
 y

15. EXAMPLE 3 Divide by a Negative Number
Solve . Then graph the solution.208  x

16. Solve the inequality. Then graph the solution
Multiply or Divide by a Negative Number.
5. 1
5
1
 p
6. 5
3
2
 x

17. Solve the inequality. Then graph the solution
Multiply or Divide by a Negative Number.
10. 12 > -5n
9. t624 

18. Assignment:

21. PROPERTIES OF INEQUALITY
Addition Property of Inequality
For all real numbers a, b, and c:
If a > b, then a + c > b + c
If a < b, then a + c < b + c
Subtraction Property of Inequality
For all real numbers a, b, and c:
If a > b, then a - c > b - c
If a < b, then a - c < b - c

22. PROPERTIES OF INEQUALITY
Multiplication Property of Inequality (c < 0)
For all real numbers a, b, and for c < 0:
If a > b, then ac < bc
If a < b, then ac > bc
Division Property of Inequality (c < 0)
For all real numbers a, b, and c < 0:
If a > b, then a ÷ c < b ÷ c
If a < b, then a ÷ c > b ÷ c