1) The document contains notes from a math class covering solving one-step inequalities using addition, subtraction, multiplication, and division. It includes examples of writing verbal phrases for inequalities and graphing the solutions. 2) Properties of inequalities are discussed, including the addition, subtraction, multiplication, and division properties. It is noted that multiplying or dividing an inequality by a negative number flips the inequality. 3) Students are assigned to practice solving inequalities using these properties and graphing the solutions.

1. Today:
Warm Up (5)
Solving One-Step Inequalities
Using Addition, Subtraction,
Multiplication & Division
Class Work
November 10, 2014

2. 1. Draw a line under each section when you first use it
this quarter, and write 2nd Qtr. Below.
2. The single biggest improvement for most notebooks is to
have more content. More warm up questions, class notes, etc.
You need to get the notes for any day you miss.
3. Some notebooks are running out of pages. Now would be
a good time to replace your notebook so you don’t have to
rewrite everything in to your new notebook for this qtr.
4. During the 2nd qtr., you will be allowed to use your
notebooks during all tests except the final exam.
Completeness and organization are particularly important.

3. 1. Unfortunately, most discussion about grades involves
what problems were wrong, what work wasn’t done,
how one could improve, etc. However....
2. Final exam grades posted. Final qtr. grades posted by Tuesday.
3. I am going to try to reserve d101 one day a week. (No
guarantees). You can BYOD; the day is reserved for Khan Academy
and our class work. If the day is productive, we will continue, the
reverse is also true.

5. There were 14 topics to master this quarter. Many of you mastered
all 14. A review of the topics for November 16...

7. Solve for y; x =
𝒚 −𝟓
𝒚+𝟐
A = -1.5
y =
𝟐𝒙 −𝟓
𝒙 −𝟏
= 16x2y2 - 21xy3 - 6x2

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

9. 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.

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

11. 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.

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

13. 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?
Checkpoint 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.

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

15. 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.

16. EXAMPLE 3 Multiply by a Negative Number
Solve . Then graph the solution.5
2
1
 y

17. EXAMPLE 4 Divide by a Negative Number
Solve . Then graph the solution.208  x

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

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

20. Assignment:

22. 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

23. 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