Solving Equations with Variables on Both Sides

30b + 53 ≥ 18b − 83

• b≥−11.3333

• b≥-14 2/3

• b>8

• -b<12

Where is the first mistake?

• Distribution of the 5

• Distribution of the 10

• subtracting 60x from both sides

• dividing by -50

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. How many miles would have to be driven in one day for both rental agencies to cost the same amount to rent?

• 120 miles

• 100 miles

• 110 miles

• 150 miles 

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

• 150x + 24 = 180 + 20x

• 150 + 24x = 180 + 20x

• 180 - 150 = 24 x + 20x

• 150 - 24x = 180 - 20x

Solve: 4k + 39 = 7k + 6

• k = 11

• k = 3

• k = -3

• k = -11

Solve: 14y + 5 = 8y - 1

• y = 1

• y = -1

Solve: 5k + 21 = 17k - 3

• k = -2

• k = 2

• k = 1.5

• k = -1.5

Solve: 45m - 38 = 5m - 158

• m = -3

• m = 3

• m = 30

• m = 2.4

Solve: 15y + 5y - 6 = 17y

• y = 2

• y = -2

• y = 9

• y = -31