3-3 Solving Inequalities Using Multiplication and Division

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3-3 Solving Inequalities Using Multiplication and Division

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.

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)

Problem 1/2: Solving an Inequality by Multiplying
π₯ 3 <β2

β 3 4 π€β₯3

π 8 > 1 4

Division Property of Inequality
Words: Let a, b, and c be real numbers with c > 0 πΌπ π > π, π‘βππ π π > π π πΌπ π < π, π‘βππ π π < π π Let a, b, and c be real numbers with c < 0 πΌπ π > π, π‘βππ π π < π π πΌπ π < π, π‘βππ π π > π π

Problem 3/4: Solving an Inequality by Dividing
β9π¦β€63

3π>6

β5π₯>β10

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?