properties of inequalities: multiplication property of inequality: multiplying each side of an...
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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