3-6A Solve Two-Step Inequalities
Name
Objective
To solve word problems involving two-step inequalities by graphing and
interpreting the answer in the context of the problem
Melba needs a large vase of 15 flowers for the head table at a banquet.
She also needs small vases of 5 flowers each for the other tables. She has
67 flowers to use. How many small vases can she fill with 5 flowers each?
! To find the number of small vases, write, solve, and graph an inequality.
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
Let t ! the number of tables.
flowers in
small vase
times
number
of tables
plus
flowers in
large vase
is less than
or equal to
67 flowers
5
•
t
"
15
#
67
Solve: 5t " 15 # 67
5t " 15 $ 15 # 67 $ 15
5t # 52
5 t # 52
5
5
t # 10.4
Graph:
!1
0
1
2
3
Use the Subtraction Property of Inequality.
Simplify.
Use the Division Property of Inequality.
Simplify.
4
5
Think
6
7
8
9
10
11
The solution set can only be the whole numbers less than or equal to 10.
You cannot have a part of a vase,
or a negative number of vases.
Therefore, only whole numbers
less than 10.4 in the solution set
are reasonable answers.
Check: According to the solution set, 5 is a solution and 12 is not.
?
5(5) " 15 # 67
Substitute 5 for t.
?
25 " 15 # 67
40 # 67 True
?
5(12) " 15 # 67
Substitute 12 for t.
?
60 " 15 # 67
75 # 67 False
So, Melba can fill up to 10 vases with 5 flowers each.
Write, solve, graph, and check an inequality for each situation. Then describe
the numbers in the solution set that are reasonable answers to each problem.
1. Lorenzo must run at least 50 miles in 2 weeks
to make the track team. After 6 days, he has run
30 miles. He wants to run the same distance on
each of the next 8 days. How far must he run
each day?
2. Jasmine and Amy go to lunch and split the total
cost, which is a whole number of dollars, evenly.
Then they each pay $12 to see a movie. In all,
they each spend less than $25. What was the
total cost of lunch?
3. Discuss and Write Why is it important to think about the real-world situation to decide
which numbers in the solution set to an inequality are reasonable solutions?
Use after SourceBook Lesson 3-6.
Chapter 3, Lesson 6A
1
3-6A Solve Two-Step Inequalities
Name
4. Hours it takes to travel to your 5. Number of coconuts you
aunt’s house
can buy
6. Change in temperature
7. Buses for a class field trip
9. Amount of a debt
8. Length of a ribbon
Write, solve, graph, and check an inequality for each situation. Then describe
the numbers in the solution set that are reasonable answers for each problem.
10. Aidan has read 43 pages of a book with
137 pages. He can read at most two pages in
one minute. How much time will it take him
to finish the book?
11. Mrs. Li needs at least 360 fluid ounces of juice
for a class brunch. She already has 128 fluid
ounces. How many cans that contain 64 fluid
ounces does she need?
12. Mr. Miller does not want to use more than
13. Jerolyn’s class has 135 oranges. They are saving
14 gallons of gasoline this week. The first 3 days
25 oranges for the members of the class. They
he used 8 gallons. If he uses same amount each
will use the rest to prepare fruit boxes by
of the remaining 4 days, how much can he use?
putting 8 oranges in each box. How many boxes
can they prepare?
14. Mr. Tobias has 78 mugs on hand in his pottery 15. Gwen had $60 at the start of her vacation. She
store. He has orders for 2 boxes of 24 mugs and
spent the same whole-dollar amount each of the
some orders for boxes of 4 mugs each. How
5 days of her trip. At the end of her trip, she
many boxes of 4 mugs can he fill?
had less than $15 left. How much did she spend
each day?
WHAT’S THE ERROR?
16. A scout leader has to figure out how many tents her troop needs for a camping trip. The
result is t % 4.25. She knows she cannot have part of a tent, so she concludes that she needs
4 or more tents. Is her conclusion correct? Explain.
2
Chapter 3, Lesson 6A
Use after SourceBook Lesson 3-6.
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
Explain what types of numbers are reasonable answers for each situation.