Beginning Algebra, 11th Edition

Step 2 Use the addition property of inequality.

Add 3.

Subtract x.

Step 3 Use the multiplication property of inequality.

Divide by 2.

x 75

2 x

2

7

10

2

2 x 710

3 x-x 7 x+ 10 - x

3 x 7 x+ 10

3 x- 3 + 37 x+ 7 + 3

156 CHAPTER 2 Linear Equations and Inequalities in One Variable

Because 2 is positive,

keep the symbol. 7

The solution set is 1 5, q 2 .Its graph is shown in FIGURE 24.

0 12345678910

FIGURE 24 NOW TRY

Solving a Linear Inequality

Solve , and graph the solution set.

Step 1

Distributive property

Combine like terms.

Step 2 Subtract 4x.

Combine like terms.

Add 15.

Combine like terms.

Step 3

Divide by 6.

Reverse the symbol.

x...- 2

• 
  

- 6 x

- 6

...

12

- 6

- 6 xÚ 12

- 6 x- 15 + 15 Ú- 3 + 15

- 6 x- 15 Ú- 3

- 2 x- 15 - 4 xÚ 4 x- 3 - 4 x

- 2 x- 15 Ú 4 x- 3

5 x- 15 - 7 xÚ 4 x- 12 + 9

51 x- 32 - 7 xÚ 41 x- 32 + 9

51 x- 32 - 7 xÚ 41 x- 32 + 9

EXAMPLE 5

The solution set is 1 - q, - 24 .Its graph is shown in FIGURE 25.

–8 –7 –6 –5 –4 –3 –2 –1 0 1

FIGURE 25 NOW TRY

OBJECTIVE 5 Solve applied problems by using inequalities.

Phrase/Word Example Inequality

Is more than A number is more than 4

Is less than A number is less than

Exceeds A number exceeds3.5

Is at least A number is at least 6

Is at most A number is at most 8 x... 8

xÚ 6

x 7 3.5

• 12 x 6 - 12

x 74

NOW TRY
EXERCISE 4
Solve the inequality, and
graph the solution set.

6 - 2 t+ 5 t... 8 t- 4

NOW TRY ANSWERS

4. 3 2, q 2

–1 012345

NOW TRY
EXERCISE 5
Solve the inequality, and
graph the solution set.

2 x- 31 x- 62641 x+ 72

5. 1 - 2, q 2

–4–3–2–1 012

Solving a Linear Inequality

Solve , and graph the solution set.

Step 1 Combine like terms and simplify.

3 x- 37 x+ 7

3 x+ 2 - 5 7-x+ 7 + 2 x

3 x+ 2 - 5 7-x+ 7 + 2 x

EXAMPLE 4

Because 6 is

negative, change

Úto ....

• 
  

The table gives some common

phrases that suggest inequality.

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