Study Guide and Intervention (continued) - MathnMind

6-2
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Study Guide and Intervention
Solving Inequalities by Multiplication and Division
Solve Inequalities by Multiplication If each side of an inequality is multiplied by
the same positive number, the resulting inequality is also true. However, if each side of an
inequality is multiplied by the same negative number, the direction of the inequality must
be reversed for the resulting inequality to be true.
For all numbers a, b, and c, with c 0,
1. if c is positive and a b, then ac bc;
Multiplication Property of Inequalities if c is positive and a b, then ac bc;
2. if c is negative and a b, then ac bc;
if c is negative and a b, then ac bc.
The property is also true when and are replaced with and .
Example 1 y
Solve 8
12.
Example 2
3
Solve k 15.
4
y
12
8
Original equation
3
k 15
4
Original equation
y
(8) (8)12 Multiply each side by 8; change to .
8
y 96 Simplify.
The solution is {y⏐y 96}.
Exercises
4 3 4
4
k 15 Multiply each side by
3
.
3 4 3
k 20 Simplify.
The solution is {k⏐k 20}.
Solve each inequality. Then check your solution.
y
1. 2
6
n
2. 22
50
3
3. h 3
5
p
4. 6
6
1
2 1
3m 3
2h
5. n 10 6. b 7. 8. 2.51 4
3 3
5 20
4
g
3 9p
n
2a
9. 2 10. 11. 5.4 12. 6
5
4 5
10
7
Define a variable, write an inequality, and solve each problem. Then check your
solution.
13. Half of a number is at least 14.
14. The opposite of one-third a number is greater than 9.
15. One fifth of a number is at most 30.
© Glencoe/McGraw-Hill 349 Glencoe Algebra 1
Lesson 6-2