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Properties of Inequalities:

Properties of Inequalities:. Lesson 3.5. Multiplication Property of Inequality: Multiplying each side of an inequality by a positive number produces an equivalent inequality.

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Properties of Inequalities:

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  1. Properties of Inequalities: Lesson 3.5 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.

  2. Properties of Inequalities: Lesson 3.5 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/c If a < b and c < 0, then a/c > b/c.

  3. 1 – n ≥ 2 8 1 n ≤ –82 –8 – 8 EXAMPLE 1 Solving an Inequality Using Multiplication Original inequality Multiply each side by –8. Reverse inequality symbol. n ≤ –16 Simplify.

  4. 15 –3m < –3 –3 EXAMPLE 2 Solving an Inequality Using Division 15 > –3m Original inequality Divide each side by –3. Reverse inequality symbol. –5 < m Simplify.

  5. 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

  6. 15,000g 61,440,000 ≤ 15,000 15,000 ANSWER Each bat eats up to 4096 grams of fruit in a year. EXAMPLE 3 Using the Division Property of Inequality 15,000g ≤ 61,440,000 Write an algebraic model. Divide each side by 15,000. g ≤ 4096 Simplify.

  7. t 1. > 4 6 t > 24 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the inequality. t 6 • > 4 • 6 Multiply each side by 6. 6 Simplify

  8. 1 x 2. – ≤ 10 2 x > –20 for Examples 1, 2, and 3 GUIDED PRACTICE Solve the inequality. Multiply both sides by -2.

  9. 27 > –3t 3. t –9 < for Examples 1, 2, and 3 GUIDED PRACTICE Solve the inequality. Divide both sides by -3

  10. 9n < 63 4. n 7 < for Examples 1, 2, and 3 GUIDED PRACTICE Solve the inequality. Divide both sides by 9

  11. ANSWER A bat can eat up to 62.5 g of figs. for Examples 1, 2, and 3 GUIDED PRACTICE 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 gof figs can it eat?

  12. Solution: Let h represent the number of hits. Write a verbal model. for Examples 1, 2, and 3 GUIDED PRACTICE 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? h Target batting average hits ≥ 0.452 ≥ 250 At bats h 250 • ≥ 0.452 • 250 250 h ≥ 113 Answer: You will have to get at least 113 hits to achieve the batting average of at least 0.452.

  13. 8n > 32 GUIDED PRACTICE Solve the inequality. -6s ≤ 54 u 6 ≥ 3 -16k ≥ 96

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