Essential Objective: At the end of this lesson, you should be able to…
 Interpret the proper inequality sign from a word problem.
 Set up and solve a word problem with an inequality.
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10.3 Word Problems with Inequalities
Name: _____________________________ Date: ______________________
Warm Up Part I: Solve each inequality and graph the solution set on the number line.
a)
2 x  10  6  2( x  3)
b)

2
12 x  6   5x  9
3
Warm Up Part II: Choose the solution set that represents each graph.
c)
d)
a.  2  x  3
b.  2  x  3
a. x  1 or x  4
b. 1  x  4
c.  2  x  3
d.  2  x  3
c. x  4 or x  1
d. x  1 or x  4
Key Concept
So far we have seen word problems involving equations. As a refresher, what are some key phrases that mean
“equals”?
What would be some key phrases that would indicate that a word problem needs to be solved using an
inequality?
Examples: Determine the proper inequality that represents each phrase:
a. The age of the tree is at least 70 years:
b. The rent is no less than $400 per month:
c. The price of the book is at most $10.95:
d. Her time in the 5k race was no more than 40 min:
e. You must be more than 40in tall to ride the ferris wheel:
The 5 step problem solving process still applies in solving word problems with inequalities with one exception:
Step 1: Read the problem carefully
Step 2: Define your variables
Step 3: SET UP THE INEQUALITY
Step 4: Solve the inequality
Step 5: Answer the question
Let’s try a few examples:
1) The Yellow Taxi Cab Co. charges a $2.75 flat rate and $.65 for each additional mile. Emma has no
more than $14 to spend on a ride. How many miles can Emma ride without exceeding her spending
limit?
2) Charlie has $500 in a savings account at the beginning of the summer, but withdraws $25 each week
to spend on meals at Duchess (his favorite). He wants to have at least $200 in the account at the end
of the summer for the start of school. How many weeks can Charlie withdraw money from the
account?
3) The length of a rectangle is 4cm longer than the width. The perimeter is no more than 28cm. What
are the maximum possible dimensions for the rectangle?
4)
The sum of two consecutive integers is less than 55. Find the pair of integers with the greatest sum.
5) The sum of two consecutive even integers is at most 400. Find the pair of integers with the greatest
sum.
Practice: Use the 5 Step Process to solve each inequality word problem.
6) The sum of three consecutive odd integers is no less than 51. What is the middle integer?
7) Find two consecutive integers such that 7 times the smaller is less than 6 times the greater. What are
the greatest such integers?
8) There are three exams given in a marking period. Ryan received an 85 and a 91 on the first two
exams. What grade must he earn on the last exam in order to get an average of no less than a 90 for
the marking period?
9) The length of a rectangle is 5 cm less than twice its width. If the perimeter of the rectangle is no more
than 70cm, what are the maximum possible dimensions?
10) The length of a rectangle is 4cm more than three times its width. If the perimeter is more than 56 cm,
what are the minimum possible dimensions of the rectangle (not allowing for fractional side
measures)?