# Solving Inequalities Using Multiplication or Division

Solving Inequalities Using Multiplication or Division 6.2 Goal Solve and graph one-step inequalities in one variable using multiplication or division Key Words multiplication property of

inequality division property of inequality PROPERTIES OF INEQUALITY Multiplication Property of Inequality (c > 0) For all real numbers a, b, and for c > 0: If a > b, then ac > bc If a < b, then ac < bc Division Property of Inequality (c > 0) For all real numbers a, b, and c > 0:

If a > b, then a c > b c If a < b, then a c < b c EXAMPL E 1 Multiply by a Positive Number a Solve 10 . Then graph the solution. 4 EXAMPL E 2 Solve: 4x > 20 Divide by a Positive Number

Then graph the solution. Checkpoint Number. Multiply or Divide by a Positive Solve the inequality. Then graph the solution 1. k 1

4 2 2. 18 2k t 3. 6 < 5 4. -21 3y PROPERTIES OF INEQUALITY Multiplication Property of Inequality (c < 0) For all real numbers a, b, and for c < 0: If a > b, then ac < bc If a < b, then ac > bc Division Property of Inequality (c < 0) For all real numbers a, b, and c < 0: If a > b, then a c < b c If a < b, then a c > b c EXAMPL E

3 Multiply by a Negative Number 1 Solve y 5 . Then graph the solution. 2 EXAMPL E 4

Divide by a Negative Number Solve 12m 18 . Then graph the solution. EXAMPL E 4 Divide by a Negative Number

Solve 8 x 20 . Then graph the solution. Checkpoint Number. Multiply or Divide by a Negative Solve the inequality. Then graph the solution 5. 1 p 1

5 2 6. x 5 3 Checkpoint Number. Multiply or Divide by a Negative Solve the inequality. Then graph the solution

1 7. k 4 4 8. -14z -70 Homework p. 333 # 16-26e, 3646e, 59-61 (15 problems)

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