Using Inequalities to Solve Problems

1 teachers like this lesson
Print Lesson


SWBAT use inequalities to solve word problems.

Big Idea

How can we sort out the important information from an inequality word problem?

Do Now

10 minutes

For each Do Now problem below, 5 is the given value, but the wording varies.  This will allow students to see how changing the wording of an inequality changes its' solution set. 

 Do Now:

Write and graph an inequality for each situation.  Give a value that would make the inequality true.

1) Kim has at least $5.

2) Elliot has more than $5.

3) Vicki has at most $5.

4) Tracy has less than $5.


After 5 minutes, I will randomly select students to show their work on the board.  

Mini Lesson

10 minutes

At this point, students should be comfortable with translating, solving and graphing inequalities.  For this lesson, students will be presented with word problems that will require their knowledge of these concepts.  Students are often intimidated by word problems, so we will discuss and analyze the problems as a class. (The word problems have been adapted from the NY Engage Common Core Curriculum.)


Example 1 - Kelly works for Quick Oil Change. If customers have to wait longer than 20 minutes for the oil change, the company does not charge for the service. The fastest oil change that Kelly has ever done took 6 minutes. Show the possible customer wait times in which the company charges the customer. 

I will give students a few minutes to read the problem to themselves and highlight the important information, before we discuss it as a class.

What are we given?

- Customers won't be charged for more than 20 minutes.

- An oil change takes 6 or more minutes.

What are we asked to find?

- The range of wait times.

What can we use to show this information?

- An inequality is useful because it can show a range of values with a minimum and maximum.

What are two inequalities we can use to represent the situation?

t ≥ 6 and t ≤ 20

How can we combine these inequalities into one inequality?

6 ≤ t ≤ 20

How can we graph this inequality?

What is a possible value for t?


Example 2 - Giselle has been babysitting to save money for a cell phone. Giselle will need to work for at least six hours to save enough money, but she must work less than 16 hours this week. Write an inequality to represent this situation, and then graph the solution. 

 For this example, I will lead students through the same process by asking questions to sort through the given information.

Group Work

10 minutes

Although students should show the work to the problems below in their own notebook, I will encourage students to discuss them with their group.


Group Work

Write an inequality for each situation.  Solve and graph the inequality.

1)  Rosalyn can make 7 cakes for a bakery each day.  So far she has orders for more than 42 cakes.  How many days will it take her to complete the orders?

2)  Lakhye saves $80 each week.  He needs to save at least $3,200 to go on his dream vacation.  How many weeks will he need to save?

3)  Ciara has less than $90.  She wants to buy 5 pairs of shoes.  What price can Ciara afford if all the shoes are the same price?


We will go over the problems in steps.  Each group will receive a white board.  First, groups will display the inequality they wrote.  Next, groups will display their steps in solving the inequality.  Third, groups will show their graph of the inequality.  For each step, we will discuss any differences that groups may have.  This is a good opportunity to compare their work with others and discuss the work further.

Exit Ticket

5 minutes

Throughout this lesson, students have worked with their classmates.  The exit ticket will be an individual assessment of students' understanding of the lesson.  I will use the results to form groups and assign both review and advanced work for students.


Exit Ticket

Write an inequality to represent the problem.  Then solve and graph your solution.

Keisha has $600 in a savings account at the beginning of the summer. She wants to have at least $300 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets.