Download Section 6.2 Solving Inequalities Using Multiplication and Division

Multiplying each side of an inequality by a ______________
positive
Equivalent inequality
number produces an _________________________.
Multiplying each side of an inequality by a ______________
negative
number and ___________________________________.
reverses the direction of the inequality
Just remember, when you multiply or divide by a
flip the inequality
negative number, _____________________.
y
9
 3 9
9
3x  12
3
y  27
x  4
|
|
|
|
|


26
27
3
28
|
|
|
|
|


-5
-4
-3
(4) s
4
 1.5 (4)
s  6
Reminder: you
must flip the
inequality
|
|
|
|
|


-7
-6
-5
reduce
16  6c
6 6
8 c
16
63
|
|
|
|
|


1
2
3
(2) r   7 (2)
2
1
2  4 x
2
2
r  7
|
|
|
|
|


-8
-7
-6
5
  4 x 2
2
1 2
5 8 x

2
2
You don’t have to
flip the inequality
because you are
dividing by a
positive number
5  8x
8
8
.625  x
|
|
|
|
|


-1
0
1
2 1
 x   5
2 3
6
2 x  5
2
3 7 21 2
  x
3 2 3 2
1 21
3  x
2 3
21  42x
2
.5  x
x  2.5
|
|
|
|
|


1
2
3
|
|
|
|
|


-1
0
1
3
6
 s
4
1
Have to flip the inequality
because we multiplied by
a negative number
4
3
6
4
  s  
3
4
1
3
 24
s
3
s  8

|
|
|
-9
-8
|
-7
|
The quotient of x and 18 is greater
than or equal to 3
x
3
18
x  54
|
|
|
|
|


54
54
55
The product of -8 and c is less than -28
 8c  28
 28
c
8
7
c
2
c  3.5
|
|
|
|
|


2
3
4
1
3
The product of d and  is less than 
4
2
1
3
 d
4
2
1d  6
d 6
|
|
|
|
|


5
6
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.
7.50x  45
x6
6 pizzas
1
1
3
Marathon: You ran a 26
mile marathon in
4
4
hours.
Write and solve an inequality to describe the average speeds s of
runners who were faster than you.
1
1
3 s  26
4
4
3.25s  26.25
s  8.08
The other runner had to have a speed
greater the 8.08 miles per hour