Equations and Inequalities with real-world scenarios

Which inequality symbol mean less than or fewer than?

• ≤

• <

• >

• ≥

Which inequality symbol means greater than or more than?

• <

• >

• ≤

• ≥

Which inequality symbol means at least or no less than?

• ≥

• >

• <

• ≤

Which inequality symbol means at most or no more than?

• <

• ≤

• >

• ≥

The greatest weight a truck can carry is 1,600 pounds. The truck is loaded with a piano that weight 400 pounds and other boxes that weight 50 pounds each. Which inequality represents all possible values of x , the number of boxes that can be loaded into the truck?

• 50x + 400 ≤ 1,600

• 50x + 400 ≥ 1,600

• 400x + 50 ≤ 1,600

• 400x + 50 ≥ 1,600

Giovanni's dad gave him 200 baseball cards to start a collection. Each week, Gio plans to add 25 more to his collection. Which inequality can be used to find w, the number of weeks it will take him to have more than 750 cards?

• 200w + 25 < 750

• 25w +200 < 750

• 200w+ 25 > 750

• 25w + 200 > 750

Mark bought a bottle of water for $2. He also bought some hotdogs for $3 each. He did not spend more than $14 on the hotdogs and water. Which inequality can be used to find h, the number of hotdogs that Mark could have bought?

• 3h - 2 ≤ 14

• 3h + 2 ≤ 14

• 3h - 2 ≥ 14

• 3h + 2 ≥ 14

Which situation can be represented by this equation?

250 + 65x = 575

• Mia is traveling to a location that is 575 miles away. She has already traveled 250 miles. What is x, the number of hours that Mia will need to travel at a speed of 65 miles per hour to reach the location?

• Mia is traveling to a location that is 575 miles away. She has already traveled 250 miles. What is x, the number of additional miles that Mia will need to travel?

• Mia is reading a book with 575 pages. She has already read 65 pages and will read 250 pages per day. What is x, the number of days that Mia will need to read to finish the book?

• Mia is reading a book with 575 pages. She has already read 315 pages. What is x, the number of pages that Mia has left to read to finish the book?

Which situation can be represented by this inequality?

120 ≤ 12k + 29

• Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. She collects buttons for "k" years. For what values of "k" will Felicia have at least 120 buttons?

• Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. She collects buttons for "k" years. For what values of "k" will Felicia have at least 120 buttons?

• Felicia has 29 buttons in her collection. She will collect 12 new buttons every year. She collects buttons for "k" years. For what values of "k" will Felicia have at most 120 buttons?

• Felicia has 12 buttons in her collection. She will collect 29 new buttons every year. She collects buttons for "k" years. For what values of "k" will Felicia have at most 120 buttons?

Which situation can be represented by this inequality?

1.25x - 6.50 > 50

• Stefen spends $6.50 on supplies for a lemonade stand and sells each cup of lemonade for $1.25. What is x, the number of cups of lemonade he must sell to earn a profit of more than $50?

• Stefen has a balance of $6.50 in his savings account and deposits $1.25 each week. What is x, the number of weeks he must deposit $1.25 in order to have a balance of more than $50 in his savings account?

• Stefen earns 1.25% interest on the balance on his account and has to pay a monthly charge of $6.50. What is x, the balance that Stefen must have in his account in order to have an ending balance greater than $50 after interest and fees?

• Stefen charges $1.25 for gasoline plus $6.50 per hour for mowing lawns. What is x, the number of hours he has to mow lawns in order to earn more than $50?