01/21/25 Write Inequalities with Variables on Both Sides

Caroline’s hair is 7 inches long and grows about 1/5 inch each month. Trinity’s hair is 10 inches long and grows about 1/10 inch each month. How many months will it take for Caroline’s hair to be at least as long as Trinity’s hair?

Choose the inequality that could be used to solve the problem.

A puppy weighs 2.8 pounds at birth and gains about 0.5 pounds per week. A kitten weighs 1.4 pounds at birth and gains about 1.2 pounds per week. In how many weeks will the weight of the kitten be no less than the weight of the puppy?

Choose the inequality that could be used to solve the problem.

Sarah plans to sell decorative signs at an upcoming craft market. It costs her $3.50 to make each sign, and she paid a one-time fee of $185 to rent her booth at the market. If Sarah sells each sign for $15.75, which inequality could be used to find the number of signs she needs to sell for her expenses to be no more than her earnings?

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TEKS.MATH.7.10A

Joe’s Catering Company charges a $45 set-up fee plus $12.50 per person. Jimmy’s catering company charges a $75 set up fee plus $7.50 per person. Which inequality could be used to determine x, the number of people for which Joe’s Catering Company would be less expensive than Jimmy’s catering company?

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TEKS.MATH.7.10A

Norah has never lost a tooth, but she will receive $0.75 from the tooth fairy each time she loses a tooth. Kate has $1.25 from the tooth fairy, and she gets $0.25 each time she loses a tooth. Which inequality could be used to find x, the number of teeth that each girl would have to lose for Norah to have at least as much money from the tooth fairy as Kate?

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TEKS.MATH.7.10A

• The ground near Brad’s house is covered with 3 inches of snow and gains 1/3 of an inch every hour. The ground near Wendy’s house is covered with 8 inches of snow and loses 2/3 of an inch every hour. After how many hours will the ground near Brad’s house be covered with more snow than the ground near Wendy’s house?

• A snail is 3 inches up a tree and climbs 1/3 inch higher every minute. A beetle is 8 inches up a tree and climbs 2/3 inch lower every minute. After how many minutes will the snail be above the beetle?

• Both problems can be solved using the inequality.

• Neither problem can be solved using the inequality.

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TEKS.MATH.7.10A

Kim’s pet-sitting company boards pets for extended stays and charges an initial fee of $100 plus $25 per night. Alfredo’s pet-sitting company boards pets for a flat rate of $50 per night. Which inequality could be used to determine x, the number of days for which Kim’s company would be less expensive than Alfredo’s company?

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TEKS.MATH.7.10A

Seth’s grandma pays him $3.75 for each bag he fills with leaves from raking her lawn. Alex already has $10 from his parents, and they are going to pay him $2 for every bag of leaves he fills from the yard. Which inequality could be used to find x, the number of bags of leaves each boy would have fill for Seth to have at least as much money from raking leaves as Alex?

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TEKS.MATH.7.10A

• Jamie is growing at an average rate of 1/2 inch each month. Marcus is 1/4 inch taller than Jamie

  and growing at an average rate of 2 inches each month. If they both continue to grow at the same rate, after how many months will Jamie be taller than Marcus?

• Springtown has had no previous rainfall this month and is currently getting 1/2 inch of rain each hour. Greenville has had 2 inches of rain this month and is currently getting 1/4 inch of

  rain each hour. If the rain continues at the same rate, after how many hours will Springtown have more rain than Greenville?

• Both problems can be solved using the inequality.

• Neither problem can be solved using the inequality.

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TEKS.MATH.6.9A

Maribel’s parents pay her an allowance of $15 per week plus $3 per chore completed. Peg’s parents pay her $6 per chore completed. Which inequality could be used to determine x, the number of chores in one week for which Peg would earn more than Maribel?

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TEKS.MATH.7.10A