Properties of Inequalities: Multiplication Property of Inequality: Multiplying each side of an inequality by a positive number produces an equivalent inequality.

Properties of Inequalities:Properties of Inequalities:

Multiplication Property of Inequality:

Multiplying each side of an inequality by a positive number produces an equivalent inequality.

Multiplying each side of an inequality by a negative number and reversing the direction of the inequality symbol produces an equivalent inequality.

If a < b and c > 0, then ac < bc.If a < b and c < 0, then ac > bc.

Lesson 3.5

Properties of Inequalities:Properties of Inequalities:

Division Property of Inequality:

Dividing each side of an inequality by a positive number produces an equivalent inequality.

Dividing each side of an inequality by a negative number and reversing the direction of the inequality symbol produces an equivalent inequality.

If a < b and c > 0, then a/c < b/cIf a < b and c < 0, then a/c > b/c.

Lesson 3.5

EXAMPLE 1 Solving an Inequality Using Multiplication

Original inequality

Multiply each side by –8. Reverse inequality symbol.

Simplify.n ≤ –16

18

n ≥ 2 –

–8 18

– n ≤ –8 2

EXAMPLE 2 Solving an Inequality Using Division

Original inequality

Divide each side by –3. Reverse inequality symbol.

Simplify.–5 < m

15 > –3m

15–3 < –3m

–3

EXAMPLE 3 Using the Division Property of Inequality

Biology

About 15,000 fruit-eating bats live on Barro Colorado Island. Yearly they eat up to 61,440,000 grams of fruit. Write and solve an inequality to find about how many grams g of fruit each bat eats yearly.

SOLUTION

EXAMPLE 3 Using the Division Property of Inequality

Write an algebraic model.

Divide each side by 15,000.

Simplify.g ≤ 4096

15,000g ≤ 61,440,000

15,000g15,000 ≤

61,440,00015,000

Each bat eats up to 4096 grams of fruit in a year.

ANSWER

GUIDED PRACTICE for Examples 1, 2, and 3

Solve the inequality.

1. t6

> 4

t > 24

6 • t 6 > 4 • 6 Multiply each side by 6.

Simplify

GUIDED PRACTICE for Examples 1, 2, and 3

Solve the inequality.

2. 12

– x ≤ 10

x > –20

Multiply both sides by -2.

GUIDED PRACTICE for Examples 1, 2, and 3

Solve the inequality.

3. 27 > –3t

t<–9

Divide both sides by -3

GUIDED PRACTICE for Examples 1, 2, and 3

Solve the inequality.

4. 9n < 63

7<n

Divide both sides by 9

GUIDED PRACTICE for Examples 1, 2, and 3

5. Fruit Bats

A bat that weighs about 25 grams can eat up to 2.5 times its body mass in figs in one night. How many grams g of figs can it eat?

A bat can eat up to 62.5 g of figs.ANSWER

GUIDED PRACTICE for Examples 1, 2, and 3

6. Baseball

If you are at-bat 250 times this baseball season, how many hits must you get to have a batting average of at least 0.452?

Let h represent the number of hits. Write a verbal model.

Solution:

hitsAt bats

≥Target batting average

h

250≥ 0.452

250 • h250 ≥ 0.452 • 250

h ≥ 113

Answer: You will have to get at least 113 hits to achieve the batting average of at least 0.452.

GUIDED PRACTICE

Solve the inequality.

8n > 32

u6 ≥ 3

-6s ≤ 54

-16k ≥ 96