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Published byGordon Hardy Modified over 9 years ago

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**3-3 Solving Inequalities Using Multiplication and Division**

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Multiplying or dividing by a negative number changes the meaning of the inequality. You need to reverse (flip) the inequality symbol to make the inequality true.

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**Multiplication Property of Inequality**

Words: Let a, b, and c be real numbers with c > 0 If a > b, then ac > bc If a < b, then ac < bc ex: -2(2) < 3(2) Let a, b, and c be real numbers with c < 0 If a > b, then ac < bc If a < b, then ac > bc ex: 3(-1) < 1(-2)

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**Problem 1/2: Solving an Inequality by Multiplying**

π₯ 3 <β2

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β 3 4 π€β₯3

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π 8 > 1 4

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**Division Property of Inequality**

Words: Let a, b, and c be real numbers with c > 0 πΌπ π > π, π‘βππ π π > π π πΌπ π < π, π‘βππ π π < π π Let a, b, and c be real numbers with c < 0 πΌπ π > π, π‘βππ π π < π π πΌπ π < π, π‘βππ π π > π π

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**Problem 3/4: Solving an Inequality by Dividing**

β9π¦β€63

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3π>6

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β5π₯>β10

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**You walk dogs in your neighborhood after school. You earn $4**

You walk dogs in your neighborhood after school. You earn $4.50 per dog. How many dogs do you need to walk to earn at least $75?

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