Properties of Inequalities

Properties of Inequalities
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This slide discusses the multiplication property of inequalities. It notes that multiplying each side of an inequality by a positive number produces an equivalent inequality, while multiplying each side of an inequality by a negative number and reversing

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About Properties of Inequalities

PowerPoint presentation about 'Properties of Inequalities'. This presentation describes the topic on This slide discusses the multiplication property of inequalities. It notes that multiplying each side of an inequality by a positive number produces an equivalent inequality, while multiplying each side of an inequality by a negative number and reversing. The key topics included in this slideshow are . Download this presentation absolutely free.

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Slide1Properties 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

Slide2Properties 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/c If a < b and c < 0, then  a/c > b/c. Lesson 3.5

Slide3EXAMPLE 1Solving an Inequality Using Multiplication Original inequality Multiply each side by  –8 . Reverse inequality symbol. Simplify. n  ≤ –16 1 8 n  ≥ 2 – –8 1 8 – n  ≤  –8     2

Slide4EXAMPLE 2Solving an Inequality Using Division Original inequality Divide each side by  –3 . Reverse inequality symbol. Simplify. –5  < m 15 > –3 m 15 –3 < –3 m –3

Slide5EXAMPLE 3Using 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

Slide6EXAMPLE 3Using the Division Property of Inequality Write an algebraic model. Divide each side by  15,000 . Simplify. g  ≤ 4096 15,000 g  ≤  61,440,000 1 5,000 g 15,000 ≤ 61,440,000 15,000 Each bat eats up to  4096  grams of fruit in a year. ANSWER

Slide7GUIDED PRACTICEfor Examples 1, 2, and 3 Solve the inequality. 1. t 6 > 4 t > 24 6 •  t 6 > 4 • 6 Multiply each side by 6. Simplify

Slide8GUIDED PRACTICEfor Examples 1, 2, and 3 Solve the inequality. 2. 1 2 – x ≤ 10 x >  –20 Multiply both sides by -2.

Slide9GUIDED PRACTICEfor Examples 1, 2, and 3 Solve the inequality. 3. 27 > –3 t t < –9 Divide both sides by -3

Slide10GUIDED PRACTICEfor Examples 1, 2, and 3 Solve the inequality. 4. 9 n  < 63 7 < n Divide both sides by 9

Slide11GUIDED PRACTICEfor 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

Slide12GUIDED PRACTICEfor 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: hits At bats ≥ Target batting average h 250 ≥ 0.452 250 • h 250 ≥ 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.

Slide13GUIDED PRACTICESolve the inequality. 8 n  > 32 u 6 ≥ 3 -6s ≤ 54 -16k ≥ 96