Intermediate Algebra (11th edition)

102 CHAPTER 2 Linear Equations, Inequalities, and Applications

STUDY SKILLS

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In math, “study cards” can help you remember
terms and definitions, procedures, and concepts.
Use study cards to

N Quickly review when you have a few minutes;

N Review before a quiz or test.

One of the advantages of study cards is that you
learn while you are making them.

Vocabulary Cards

Put the word and a page reference on the front of
the card. On the back, write the definition, an exam-
ple, any related words, and a sample problem (if
appropriate).

Procedure (“Steps”) Cards

Write the name of the procedure on the front of
the card. Then write each step in words. On the
back of the card, put an example showing each
step.

Make a vocabulary card and a procedure card for
material you are learning now.

Using Study Cards

Interval notation p. 91

Front of

Card

Back of

Card

Definition: Using symbols to describe an interval on a number

line.

Examples: (5, )

Use interval notation to tell what numbers are in the solution set

for an inequality.

All numbers greater than 5,

not including  5

[5, 5) All numbers between including 5 and 5,

5, excluding 5

Symbols: ( ) [ ] ( ] [ )

p. 95 Front of

Card

Solving a Linear Inequality

1. Simplify each side separately. (clear parentheses and combine
   like terms.)


2. Isolate variable terms on one side. (Add or subtract the same
   number from both sides.)


3. Isolate the variable. (Divide both sides by the same number; if
   dividing by a negative number, reverse direction of inequality.)

Back of

Card

Solve 3 (x  4)  (^2)  (^7)  x and graph the solution set.
3 (x  4) ^2 ^7  x
3x ^12 ^2 ^7  x
3x ^10  x ^7  x  x
2x ^10 ^10 ^7 ^10
2x
 2
3x ^10 ^7  x
2x ^10 ^7
Clear parentheses.
Combine like terms.
Both sides are simplified.
Add x to both sides.
Variable term still not isolated.
Add 10 to both sides.

^9 ^8

8

17

 2

17

x 2



17

 2

1

 2

Divide both sides by – 2; dividing

by negative, reverse direction of

inequality symbol.

Each exercise requires the graph of two inequalities. Graph them and respond to the state-

ment that follows. See Section 1.1.

73. (a)Graph
    (b)Graph
    (c)Describe the set of numbers belonging to bothof these sets.


74. (a)Graph
    (b) Graph
    (c) Describe the set of numbers belonging to eitherof these sets.

x 6 9.

x 6 7.

x 6 5.

x 7 4.

PREVIEW EXERCISES