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Inequalities
3A Simple Inequalities
3-1 Graphing and Writing
Inequalities
3-2 Solving Inequalities by Adding or
Subtracting
3-3 Solving Inequalities by
Multiplying or Dividing
3B Multi-Step and Compound
Inequalities
3-4 Solving Two-Step and Multi-Step
Inequalities
3-5 Solving Inequalities with
Variables on Both Sides
Lab Truth Tables and Compound
Statements
3-6 Solving Compound Inequalities
Ext Solving Absolute-Value
Inequalities
For a Good Cause
You can use the concepts in this
chapter to plan for a fund-raising
event. Inequalities help you determine
how to reach your fund-raising goals.
KEYWORD: MA7 ChProj
164 Chapter 3
Vocabulary
Match each term on the left with a definition on the right.
1. equation A. mathematical phrase that contains operations, numbers,
2. evaluate and/or variables
3. inverse operations B. mathematical statement that two expressions are equivalent
4. like terms C. value of a variable that makes a statement true
5. solution of an D. terms that contain the same variable raised to the same power
equation E. to find the value of an expression
F. operations that “undo” each other
Evaluate Expressions
Evaluate each expression for a = 2 and b = 6.
6. b-a 7. ab 8. b÷a 9. a+b
Compare and Order Real Numbers
Compare. Write <,>, or =.
1 2
10. 10 21 11. 5.27 5.23 12. 20% 0.2 13. _ _
3 5
Combine Like Terms
Simplify each expression by combining like terms.
14. 6x+x 15. -8a+ 3a
16. 9x2 - 15x2 17. 2.1x + 4.3x
Distributive Property
Simplify each expression.
( ) ( )
18. 2 x + 3 19. 3- d 5
( ) ( )
20. 4 r - 1 21. 3 4 + m
Solve One-Step Equations
Solve.
h
22. s - 3 = 8 23. -7x= 21 24. y + 11 = 2 25. _= 6
2
y
26. t + 2 =-2 27. 6x= 42 28. r- 8 =-13 29. _=-12
3
Inequalities 165
Key
Vocabulary/Vocabulario
Previously, you compound inequality desigualdad compuesta
learned the properties of
•
equality. inequality desigualdad
solved equations by using
• intersection intersección
inverse operations.
solved equations with solution of an inequality solución de una
• desigualdad
variables on both sides.
union unión
Vocabulary Connections
You will study To become familiar with some of the
vocabulary terms in the chapter, consider
the properties of inequality.
• the following. You may refer to the chapter,
how to solve inequalities by the glossary, or a dictionary if you like.
•
using inverse operations. 1. The prefix in- means “not.” An equality
how to solve inequalities with
• states that two things are equal. Use
variables on both sides. these meanings to write your own
how to solve compound definition for the word inequality .
•
inequalities. 2. The word compound means “consisting
of two or more parts.” What do you think
a compound inequality might be?
3. The intersection of two roads is the
place where the two roads overlap. What
do you think the intersection of two
You can use the skills in graphs would be?
this chapter 4. The word union begins with the root
in all your future math uni-. List some other words that begin
•
classes, including Geometry. with uni-. What do all of these words
in other classes, such as have in common?
•
Health, Chemistry, Physics,
and Economics.
in the real world to plan a
•
budget, to find cost-efficient
services, and to set financial
goals.
166 Chapter 3
Study Strategy: Use Your Notes Effectively
Taking notes helps you arrange, organize, and process information from your
textbook and class lectures. In addition to taking notes, you need to use your
notes before and after class effectively.
n
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e
Step 1: Before Class 3 L
/
• Review your notes 10
e similar?
es ar
w if figur
from the last class. o I kno
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Ho
• Then preview the e
b
y
t ma
hape, bu
next lesson and write es—same s
Similar figure Step 3: After Class
down any questions t same siz
no • Fill in the holes you
you have. es—same left during class.
es and angl
nding sid
espo
Corr n. • Highlight or circle
e positio
tiv
ela
r the most important
nal ideas, such as
e proportio
es ar
. sid
es if corr
Similar figur e same. vocabulary,
es ar
. angl formulas, or
Step 2: During Class and corr
• Write down main e sim. procedures.
es ar
w figur
ho
o s
∼ t
ideas. he symbol
e t
s
U • Use your notes to
• If you miss something, quiz yourself.
leave a blank and B E
keep taking notes. Fill C
BC A
B _ _
A
in any holes later. _=EF=DF
• Use diagrams and DE D
∠
abbreviations. A C m∠A m
∠E
Make sure you will m∠B m
∠F
understand any F m∠C m
abbreviations later. D DEF
BC ∼△
A
△
Try This
1. Look at the next lesson in your textbook. Write down some questions you have
about the material in that lesson. Leave space between each question so that you
can write the answers during the next class.
2. Look at the notes you took during the last class. List three ways you can improve
your note-taking skills.
Inequalities 167
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