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 𝑥 3 <−2

− 3 4 𝑤≥3

𝑐 8 > 1 4

Division Property of Inequality Words: Let a, b, and c be real numbers with c > 0 𝐼𝑓 𝑎 > 𝑏, 𝑡ℎ𝑒𝑛 𝑎 𝑐 > 𝑐 𝑐 𝐼𝑓 𝑎 < 𝑏, 𝑡ℎ𝑒𝑛 𝑎 𝑐 < 𝑐 𝑐 Let a, b, and c be real numbers with c < 0 𝐼𝑓 𝑎 > 𝑏, 𝑡ℎ𝑒𝑛 𝑎 𝑐 < 𝑐 𝑐 𝐼𝑓 𝑎 < 𝑏, 𝑡ℎ𝑒𝑛 𝑎 𝑐 > 𝑐 𝑐

Problem 3/4: Solving an Inequality by Dividing −9𝑦≤63

3𝑚>6

−5𝑥>−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?