4.3 The Multiplication Property of Inequality

1. 4.3 The Multiplication Property of Inequality • Goal: To solve inequalities using the multiplication property

2. Multiplication Property of Inequalities For all rational numbers a, b, and c: • When c is positive, if a > b, then a • c > b • c • When c is negative, if a > b, then a• c < b • c

3. If you multiply or divide an inequality by a negative number, reverse the inequality sign in the answer.

4. Caution! Do not change the direction of the inequality symbol just because you see a negative sign. For example, you do not change the symbol when solving 4x < –24.

5. –8 –2 –10 –6 –4 0 2 4 6 8 10 Check It Out! Solve the inequality and graph the solutions. Check your answer. 10 ≥ –x divide both sides by –1 to make x positive. Change  to . –1(10) ≤ –1(–x) –10 ≤ x

6. Check Check a number greater than 10. Check the endpoint, –10. 10 = –x 10 ≥ –x 10 –(–10) 10 ≥ –(11)  10 10  10 ≥ –11 Check It Out! Solve the inequality and graph the solutions. Check your answer. 10 ≥ –x

7. 6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. -3y  12 -3 -3 y  -4 

8. 6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. -4y  16 y  -4

9. 6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. 3y  -15 y  -5

10. 6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. -5y  -20 y  4

11. Since x is divided by –3, multiply both sides by –3. Change to . 10 14 16 18 20 22 24 26 28 30 12 Solve the inequality and graph the solutions. 24  x (or x  24)

12. Assignment Pg 182 (2-42) even