Section 6.2Solving Inequalities Using

Multiplication and Division

Multiplying each side of an inequality by a ______________ number produces an _________________________.

Multiplying each side of an inequality by a ______________ number and ___________________________________.

positiveEquivalent

inequality

negativereverses the direction of the

inequality

Just remember, when you multiply or divide by a negative number, _____________________.flip the inequality

39y

9 9

27y

| | | | | 27 2826

3 12x

4x

3 3

| | | | | -4 -3-5

1.54s

( 4) ( 4)

6s Reminder: you must flip the inequality

| | | | | -6-7 -5

| | | | | 21 3

16 6c6 6166

c

reduce

83

72 2r

(2)(2)

7r

| | | | | -7-8 -6

12 42

x

452

x 1

22

5 82 2

x

5 8x 8 8

You don’t have to flip the inequality because you are dividing by a positive number .625 x

| | | | | 0-1 1

1 53 6x

22

2 5x 2 2

2.5x

| | | | | 21 3

1 2132 3

x 33

22

7 212 3

x

21 42x

.5 x

| | | | | 0-1 1

16

43

s

34

16

43

34

s

324

s

8s

Have to flip the inequality because we multiplied by a negative number

| | | | | -8-9 -7

The quotient of x and 18 is greater than or equal to 3

318x

| | | | | 5454 55

54x

The product of -8 and c is less than -28

288 c

828

c

27

c

5.3c

| | | | | 32 4

23

41

thanlessisanddofproductThe

23

41

d

61 d

6d| | | | |

65 7

Pizza Party: You have a budget of $45 to buy pizza for a student council meeting. Pizzas cost $7.50 each. Write and solve an inequality to find the possible numbers of pizzas that you can buy.

4550.7 x

6x

pizzas6

Marathon: You ran a 4126 mile marathon in 4

13 hours.

Write and solve an inequality to describe the average speeds s of runners who were faster than you.

4126

413 s

25.2625.3 s

08.8sThe other runner had to have a speed greater the 8.08 miles per hour