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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