Name
Class
3-3
Date
Reteaching
Solving Inequalities Using Multiplication or Division
You can solve inequalities using multiplication or division using these two
important rules.
• You can multiply or divide each side of an inequality by a positive number.
• You can multiply or divide each side of an inequality by a negative number
only if you reverse the inequality sign.
Problem
c
What are the solutions of 5 # 22? Graph the solutions.
c
Original inequality
5 # 22
c
5 Q 5 R # 5(22)
Multiply each side by 5. Keep the inequality symbol the same.
c # 210
Simplify.
To graph c # 210, place a closed circle at 210 and shade to the left.
0
1612 8 4
4
Problem
What are the solutions of 2 23 t . 4? Graph the solutions.
223 t . 4
Original inequality
3
3
22 Q223 t R , 22(4)
3
Multiply each side by 22 . Reverse the inequality symbol.
t , 26
Simplify.
To graph t , 26, place an open circle at 26 and shade to the left.
8 6 4 2
0
2
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Name
Class
Date
Reteaching (continued)
3-3
Solving Inequalities Using Multiplication or Division
Problem
What are the solutions of 26h # 239? Graph the solutions.
26h # 239
Original inequality
26h
239
26 $ 26
h $ 612
Divide each side by 26. Reverse the inequality symbol.
Simplify.
To graph h $ 612 , place closed circle at 612 and shade to the right.
2
0
2
4
6
8
Exercises
Solve each inequality. Graph and check your solutions.
x
1. 7 . 22 x S 214
ź16
ź12
2. 8p # 32 p K 4
ź8
ź4
4
0
ź3 ź2 ź1 0 1 2 3 4 5 6 7
k
4. 22 , 25 k S 10
2
3. 5 r $ 6 r L 15
ź6 ź3 0 3 6 9 12 15 18 21 24
ź4 ź2 0 2 4 6 8 10 12 14 16
3
6. 5t . 29 t S 215
5. 23f # 12 f L 24
ź24
ź7 ź6 ź5 ź4 ź3 ź2 ź1 0 1 2 3
ź3 ź2 ź1 0 1 2 3 4 5 6 7
ź40 ź30
3
3
9. 24d , 28 d S 12
ź1
ź12
ź6
6
0
z
8. 25 $ 4 z K 220
7. 22w . 28 w R 4
ź2
ź18
ź20
ź10
0
ź2
ź1
10. 24n $ 14 n K 272
0
1
2
ź5
ź4
ź3
11. A bus company charges $2 for each trip. It also sells monthly passes for $50.
Write and solve an inequality to find how many trips you could make before
the monthly pass is cheaper.
2t S 50; For more than 25 trips, the monthly pass is cheaper.
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Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
30