Equations and Inequalities with Variables on Both Sides

Brian does not own a car, so he uses rideshare companies to get around town. - Company A charges a service fee of $5 and an additional $0.75 per mile driven. - Company B charges a service fee of $6 and an additional $0.50 per mile driven. Which equation can be used to find m, the number of miles it would take for both company A and company B to charge the same amount?

• 0.75m + 6 = 0.50m + 5

• 0.75m + 5 = 0.50m + 6

• 6m + 0.75 = 5m + 0.50

• 5m + 0.75 = 6m + 0.50

Mrs. Turner planted two fruit trees in her garden last spring. The apple tree was 32 inches when she planted it, and it grew 4 inches each month. The orange tree was 28 inches when she planted it, and it grew 6 inches each month. Which inequality can be used to find m, the number of months it will take for the height of the orange tree to be no less than the height of the apple tree?

• 28 + 6m ≤ 32 + 4m

• 28 + 6m < 32 + 4m

• 28 + 6m > 32 + 4m

• 28 + 6m ≥ 32 + 4m

Tags

CCSS.7.EE.B.4B

Which situation can be represented by this inequality? 100 + 25x > 175 + 20x

• Darlene has $100 in her savings account and deposits $25 each week. Stanley has $175 in his savings account and deposits $20 each week. After how many weeks will Darlene and Stanley have the same amount of money in their savings accounts?

• Darlene has $100 in her savings account and deposits $25 each week. Stanley has $175 in his savings account and deposits $20 each week. After how many weeks will Darlene have less money in her savings account than Stanley has in his savings account?

• Darlene has $100 in her savings account and deposits $25 each week. Stanley has $175 in his savings account and deposits $20 each week. After how many weeks will Darlene have more money in her savings account than Stanley has in his savings account?

• Darlene has $100 in her savings account and deposits $20 each week. Stanley has $175 in his savings account and deposits $25 each week. After how many weeks will Darlene have more money in her savings account than Stanley has in his savings account?

Kiara and Donovon attend different middle schools. They both went to their schools’ winter carnivals. Kiara paid a $5 entrance fee and bought several tickets costing $0.75 each for games and rides. Donovon paid a $7 entrance fee and bought several tickets costing $0.50 each for games and rides. How many tickets, x, must Kiara and Donovon each buy in order for the cost of attending their school carnivals to be the same?

• 8 tickets

• 10 tickets

• 28 tickets

• 48 tickets

Tags

CCSS.8.EE.C.7B

A pet store has two large fish tanks to contain its aquatic animals. Tank A contains 250 gallons of water and is being drained at a rate of 2 gallons per minute. Tank B is empty and is being filled at a rate of 3 gallons per minute. Which inequality can be used to find x, the number of minutes it will take for tank A to contain less water than tank B?

• 250 + 2x < 3x

• 250 - 2x > 3x

• 250 + 2x > 3x

• 250 - 2x < 3x

A square is shown. What value of s makes the sides of the square congruent?

• 0.17

• 3.5

• 18

• 2.1

Tags

CCSS.8.EE.A.2

Which situation can be represented using this equation? 45 + 3h = 63 - 2h

• The temperature in Culver City is 45°F and is increasing 3° every hour. The temperature in Temple Town is 63°F and is decreasing 2° every hour. After how many hours, h, will the temperatures in Culver City and Temple Town be the same?

• The temperature in Culver City is 45°F and is decreasing 3° every hour. The temperature in Temple Town is 63°F and is increasing 2° every hour. After how many hours, h, will the temperatures in Culver City and Temple Town be the same?

• The temperature in Culver City is 45°F and is increasing 2° every hour. The temperature in Temple Town is 63°F and is decreasing 3° every hour. After how many hours, h, will the temperatures in Culver City and Temple Town be the same?

• The temperature in Culver City is 3°F and is increasing 45° every hour. The temperature in Temple Town is 2°F and is decreasing 63° every hour. After how many hours, h, will the temperatures in Culver City and Temple Town be the same?

Tags

CCSS.8.EE.C.7B

What is the solution to the equation? -1.2x + 6 = x - 13.8

• x = -4.8

• x = 99

• x = 9

• x = 3.5

Which situation can be represented by this inequality? 5c + 2 > 8c

• The cost of 5 candy bars is greater than the cost of 8 candy bars and a $2 soda.

• The cost of 5 candy bars and a $2 soda is greater than the cost of 8 candy bars.

• The cost of 5 candy bars and a $2 soda is less than the cost of 8 candy bars.

• The cost of 8 candy bars is greater than the cost of 5 candy bars and a $2 soda.

Tags

CCSS.7.EE.B.4B