Equations and Inequalities on Both Sides

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

Blind company A charges $25.00 to install blinds for one room and $5.00 for each additional window. Blind company B charges $30.00 to install blinds in one room and $4.00 for each additional window. Write an equation to determine how many blinds would need to be installed for the price to be equal.

• 25 + 5x = 30 + 4x

• 25 - 5x = 30 - 4x

• 30 - 25 = 4x + 5x

• 25x + 5 = 30x + 4

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 

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

What is the solution to this equation? (3/4)x + 7 = (x/4) - 8. Enter your answer in the box.

Mathematical Equivalence

ON

The equation 9x + 1 = 4x + 16 is modeled.  Which answer represents the solution to the equation?

• 3

• 3.4

• -3

• none of these

Mathematical Equivalence

ON

• x < 1
• x < -1
• x > 1
• x > -1

Identify the type of solution.

• Infinite solutions

• One solution

• No solution