Solving Equations and Inequalities with Variables on Both Sides

Carol wants to join a dance studio. Studio A charges $100.00 for the entry fee and $45.00 per class, while Studio B charges $125.00 for the entry fee and $30.00 per class.  Write an equation to determine how many classes would need to be taken for the price to be equal? 

• 125 - 100 = 45x + 30x
• 100x + 45 = 125x + 30
• 100 + 45x = 125 + 30x
• 100 - 45x = 125 - 30x 

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. Which equation could be used to determine how many miles would have to be driven in one day for both rental agencies to cost the same amount to rent? 

• 30 + 0.15x = 36 + 0.10x
• 30 - 0.15x = 36 - 0.10x
• 30 + 36 = 0.10x + 0.36x
• 36 - 30 = 0.36x + 0.10x

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

Write an inequality to represent the following relationship:
Three times a number minus two is less than the number plus ten.

• 3x - 2 < x + 10
• 2 - 3x < x + 10
• 3x - 2 > x + 10
• 2 - 3x > x + 10

What inequality symbol is used in:
384 + 2x < 6x?

• Greater Than
• Less Than
• Greater Than or Equal To
• Less Than or Equal To

Select the situation that could be modeled by: 2x + 4 = 3x

• The number of students in the 2-year-old class and the 4-year-old class equals the number of students in the 3-year-old class. How many students are in each class?
• Cade bought 2 books for $4 each and Clara bought 3 books. How much did Clara pay?
• Dean is 4 more than twice his brother’s age. He is also 3 times his brother’s age. How old is Dean’s brother?

Select the situation that could be modeled by: 12 + 5x = 18+3x

• Derek charges a base fee of $12 to walk a dog plus $5 per hour. Darla charges a base fee of $18 plus $3 an hour to walk a dog. After how many hours would they make the same amount of money?
• Andy buys 12 sodas for $5 each. Alex buys 18 sodas for $3 each. If they each spent the same amount, how much did they spend?
• Brian charges $12 for a hat and $5 per shirt. Blake buys 3 hats and 18 shirts. How many hats and shirts must they sell to make the same amount of money?

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x
• 30x + 20 < 15x + 30
• 30 + 20x > 15 + 30x
• 30x + 20 > 15x + 30

is 7 a solution to the equation
3x+8-x=5x-4

• yes
• no
• maybe

10x + 9 = 4x - 9

• 0
• 3
• -3
• -18