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. Solve the inequality and graph the solutions. Check your answer.
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
–10 –8 –6 –4 –2 2 4 6 8 10

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

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

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

9. Solve for “y”, then graph the solution.-2 -6 -4 6 4 2

10. Solve for “y”, then graph the solution.-2 -6 -4 6 4 2

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

12. Assignment Pg 182 (2-42) even