1. 6.2 Solving inequalities by multiplication
If any positive number is multiplied to each side of a true inequality, the resulting inequality is also true.
For example:
3 < 8
3(2) < 8(2)
6 < 16
Example 1:

2. Multiplication by a negative number
If any negative number is multiplied to each side of a true inequality, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.
For example:
3 < 8
3(-2) < 8(-2)
-6 > -16
Example 2:

3. Write an inequality for the sentence below.
Four-fifths of a number is at most twenty.
4/5x
4/5x
4/5x 20
Solve
4/5x 20
(5/4) 4/5x 20 (5/4)
x  100/4
x  25
{x | x < 25}

4. Division by a positive number
If each side of a true inequality is divided by the same positive number, the resulting inequality is also true.
For example:
2 < 8
2/2 < 8/2
1 < 4
Example 4:

5. Division by a negative number
If each side of a true inequality is divided by any negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.
For example:
2 < 8
2/-2 < 8/-2
-1 > -4
Example 5:

6. Try These
p even
Assignment #40
p odd, 54, 56, 57