Download 4_3 inequalities_multiplication TROUT 09

4.3 The Multiplication Property of
Inequality
• Goal: To solve inequalities using the
multiplication property
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
If you multiply or divide an
inequality by a negative
number, reverse the inequality
sign in the answer.
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.
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
0
2
4
6
8 10
Check It Out!
Solve the inequality and graph the solutions.
Check your answer.
10 ≥ –x
Check
Check the endpoint, –10.
10 = –x
10
10
–(–10)
10 
Check a number greater
than 10.
10 ≥ –x
10
10
≥ –(11)
≥ –11
Solve for “y”, then graph the solution.
-3y  12
-3 -3
y
 -4
-6
-4
-2
0
2
4
6
Solve for “y”, then graph the solution.
-4y  16
y  -4
-6
-4
-2
0
2
4
6
Solve for “y”, then graph the solution.
3y  -15
y  -5
-6
-4
-2
0
2
4
6
Solve for “y”, then graph the solution.
-5y  -20
y4
-6
-4
-2
0
2
4
6
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)
10 12 14 16 18 20 22 24 26 28 30
Assignment
Pg 182 (2-42) even