Lesson 21: Writing & Graphing Inequalities in Real-World Problems

FUSD AZCCRS MATHEMATICS CURRICULUM

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Lesson 21

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Lesson 21: Writing & Graphing Inequalities in Real-World Problems

 I can write inequalities based on real-world situations and graphs of inequalities.

 I can graph inequalities based on real-world situations and inequalities written in algebraic form.

Example 1

Statement Inequality Graph

a. Caleb has at least $5.

b. Tarek has more than $5.

c. Vanessa has at most $5.

d. Li Chen has less than $5.

Example 2

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.

Example 3

Gurnaz has been mowing lawns to save money for a concert. Gurnaz will need to work for at least six hours to save enough

money, but he must work fewer than 16 hours this week. Write an inequality to represent this situation, and then graph the

solution.

Exercises 1–5

Write an inequality to represent each situation. Then, graph the solution.

2. Blayton is at most 2 meters above sea level.

3. Edith must read for a minimum of 20 minutes.

FUSD AZCCRS MATHEMATICS CURRICULUM

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Lesson 21

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This work is licensed under a

Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

4. Travis milks his cows each morning. He has never gotten fewer than 3 gallons of milk; however, he always gets fewer than

9 gallons of milk.

5. Rita can make 8 cakes for a bakery each day. So far she has orders for more than 32 cakes. Right now, Rita needs more

than four days to make all 32 cakes.

6. Rita must have all the orders placed right now done in 7 days or fewer. How will this change your inequality and your

graph?

Possible Extension Exercises 6–10

7. Kasey has been mowing lawns to save up money for a concert. He earns $15 per hour and needs at least $90 to go to the

concert. How many hours should he mow?

8. Rachel can make 8 cakes for a bakery each day. So far, she has orders for more than 32 cakes. How many days will it take

her to complete the orders?

9. Ranger saves $70 each week. He needs to save at least $2,800 to go on a trip to Europe. How many weeks will he need to

save?

10. Clara has less than $75. She wants to buy 3 pairs of shoes. What price shoes can Clara afford if all the shoes are the same

price?

11. A gym charges $25 per month plus $4 extra to swim in the pool for an hour. If a member only has $45 to spend each

month, at most how many hours can the member swim?