Writing Multi-Step Inequalities

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?

• 12.50 + 45x ≤ 7.50 + 75x

• 45 + 12.50x < 75 + 7.50x

• 12.50x + 7.50x < 45 +75

• 45 + 12.50x > 75 + 7.50x

Tags

CCSS.7.EE.B.4B

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?

• 0.75x > 1.25 + 0.25x

• 0.75x < 1.25x + 0.25

• 0.75x ≥ 1.25 + 0.25x

• 0.75x ≤ 1.25 + 0.25x

Tags

CCSS.7.EE.B.4B

Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 25 mph and is decreasing his speed by 0.7 mph each second. Which of the following inequalities could be used to determine how long it would take for Mike to be driving no faster than Hank?

• 12 + 0.2x ≤ 25 - 0.7x

• 12 + 0.2x < 25 + 0.7x

• 12 + 0.2x > 25+ 0.7x

• 12 + 0.2x ≥ 25 - 0.7x

Tags

CCSS.7.EE.B.4B

A tree in Micah’s yard has 120 leaves and loses an average of 4.5 leaves each day. A tree in Heather’s yard has 45 leaves and gains an average of 0.5 leaves each day. Write and solve an equation to find the number of days it will take for both trees to have an equal number of leaves.

• x = 12

• x = -18.75

• x = 15

• x = -15.75

Tags

CCSS.7.EE.B.4A

-7.2x + 3.5 = -8.7x – 10

• x = -10

• x = -9

• x = -8

• x = -7

Isabella takes the bus to work. The bus ride to work costs her $2.50 each time. She could buy a bus pass for a one-time fee of $15.00 and then would only pay $1.00 each time to ride the bus. How many times would she have to take the bus in order for the cost to be the same?

• 10 times

• 12 times

• -10 times

• 15 times

Hayley has $155 in her savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each week. After how many weeks will they have the same amount?

• 2 weeks

• 3 weeks

• 4 weeks

• 5 weeks

Tags

CCSS.8.EE.C.8C