Beginning Algebra, 11th Edition

(b)

Multiply each part by 3

to clear the fraction.

Distributive property

Add 3 to each part.

Divide each part by 2.

The solution set is C- 29 ,^272 B.Its graph is shown in FIGURE 28.

-

9

2

... m 6

27

2

- 9

2

...

2 m

2

6

27

2

• 9 ... 2 m 627

- 12 + 3 ... 2 m- 3 + 3624 + 3

- 12 ... 2 m- 3 624

31 - 42 ... 3 a

2

3

m- 1 b 6 3182

• 4 ...

2

3

m- 1 68

SECTION 2.8 Solving Linear Inequalities 159

–6 – 4 –2 0 2 4 6 8 10 12 14

27

2

9

• 2

FIGURE 28 NOW TRY

Think: - 92 =- (^4 12)

NOTE The inequality in Example 8(b), can also be solved by

first adding 1 to each part and then multiplying each part by Try this.

The table summarizes methods of expressing solution sets of three-part inequalities.

3

2.

- 4 ...^23 m- 16 8,

Set-Builder Notation Interval Notation Graph

a b

5 x|a...x...b 6 3 a, b 4

a b

5 x|a...x 6 b 6 3 a, b 2

a b

5 x|a 6 x...b 6 1 a, b 4

a b

5 x|a 6 x 6 b 6 1 a, b 2

Complete solution available
on the Video Resources on DVD

2.8 EXERCISES

Concept Check Work each problem.

1. When graphing an inequality, use a parenthesis if the inequality symbol is or
   . Use a square bracket if the inequality symbol is or.


2. Trueor false? In interval notation, a square bracket is sometimes used next to an
   infinity symbol.


3. In interval notation, the set is written.


4. How does the graph of xÚ- 7 differ from the graph of x7- 7?

5 x|x 706

NOW TRY
EXERCISE 8
Solve the inequality, and
graph the solution set.

• 4 ...

3

2

x- 1 ... 0

NOW TRY ANSWER

8. C-2,^23 D

–3 –2 –1 0 1 2 3

2

3

Think:^272 = (^13 12)