LEVEL 1

Writing One-Step Inequalities

Directions: Write an inequality for each scenario. Then solve the inequality and explain your solution in the context of the problem. Don’t forget to define your variable!

  1. Rogan is compiling songs to put on a CD for his friend. He can include at most 70 minutes of music on the CD. He has already selected 45 minutes of music. How many more minutes of music can he select?
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  1. Vance wants to buy some souvenirs for his friends from his recent vacation. He found some t-shirts at a gift shop that cost $12 each and he has $70 to spend. How many t-shirts can Vance buy?

  1. Sadie wants to make several batches of chocolate chip cookies. She has 6 teaspoons of baking soda left in the container and each batch uses ¾ of a teaspoon of baking soda. How many batches of cookies can Sadie make?
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  1. Leslie hopes to be at least six feet tall (72 inches). Currently, she is 56 inches tall. How many more inches does Leslie hope to grow?

  1. Petra must write a report with more than 1,000 words for her history class. So far, she has written 684 words and the report is due tomorrow morning! How many more words does Petra need to write tonight?
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  1. A rectangle has a width of 5 inches and an area of less than 70 square inches. How many inches will the length of the rectangle be?

LEVEL 2

WritingTwo-Step Inequalities

Directions: Write an inequality for each scenario. Then solve the inequality and explain your solution in the context of the problem. Don’t forget to define your variable!

1. Matilda needs at least $112 to buy a new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve an inequality to find how many hours she will need to babysit to buy the dress. Interpret the solution. / 2. Tamara already has $55 dollars in her savings account. If she puts $5 per week in her account, write and solve an inequality to find out how many weeks she must save to have at least $100 in her account. Interpret the solution.
3. Latrell has $8 to spend on postcards. He wants to buy one large postcard and some small ones. Write and solve an inequality to find out how many small postcards Latrell can purchase. Interpret the solution.
/ 4. Remy needs at least $3,000 to buy a used car. He already has $1,800. If he saves $50 per week, write and solve an inequality to find out how many weeks he must save to buy the car. Interpret the solution.
5. Manuel earns $400 per week plus a 3% commission on everything he sells. Write and solve an inequality to find out how much he must sell to have a weekly income of at least $700. Interpret the solution. / 6. You want to spend no more than$12 on a carriage ride. The driver tells you there is an initial charge of $5 plus $0.50 per mile. Write and solve an inequality to find out how many miles you can ride. Interpret the solution.
7. Corey has 16 cups of flour to make cookies. One batch of cookies takes 2 ½ cups of flour. If he must save 6 cups of flour for other baking, write and solve an inequality to find out how many batches of cookies he can make. Interpret the solution. / 8. Sylvia needs at least $310 for a new audio system. She has already saved $120. She earns $10 per hour at her part-time job. Write and solve an inequality to find how many hours she will need to work to buy the system. Interpret the solution.

LEVEL 1 ANSWERS:

  • Definition:x = minutes of music
  • Inequality:
  • Solution:
  • Answer:Rogan can select no more than 25 minutes of music.
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  • Definition:x = number of t-shirts
  • Inequality:
  • Solution:
  • Answer:Vance can buy up to 5 t-shirts.

  • Definition:x = batches of cookies
  • Inequality:
  • Solution:
  • Answer:Sadie can make no more than 8 batches of cookies.
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  • Definition:x = number of inches
  • Inequality:
  • Solution:
  • Answer:Leslie hopes to grow at least 16 more inches.

  • Definition:x = number of words
  • Inequality:
  • Solution:
  • Answer:Petra must write more than 316 more words.
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  • Definition:x = length of rectangle (in.)
  • Inequality:
  • Solution:
  • Answer:The length of the rectangle must be less than 14 inches.

LEVEL 2 ANSWERS:

  • Definition:x = number of hours
  • Inequality:
  • Solution:
  • Answer: Matilda must babysit for at least 8 hours.
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  • Definition:x = number of weeks
  • Inequality:
  • Solution:
  • Answer:Tamara must save money for at least 9 weeks.

  • Definition:x = number of small postcards
  • Inequality:
  • Solution:
  • Answer:Latrell can buy up to 4 postcards.
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  • Definition:x = number of weeks
  • Inequality:
  • Solution:
  • Answer:Remy must save money for at least 24 weeks.

  • Definition:x = amount sold ($)
  • Inequality:
  • Solution:
  • Answer:Manuel must sell at least $10,000 of merchandise.
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  • Definition:x = number of miles
  • Inequality:
  • Solution:
  • Answer:You can ride no more than 14 miles.

  • Definition:x = cups of flour
  • Inequality:
  • Solution:
  • Answer:Corey must make less than 4 batches of cookies.
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  • Definition:x = number of hours
  • Inequality:
  • Solution:
  • Answer:Sylvia must work for at least 19 hours.