Model and Solve Variables on Both Sides

Solve:

8x - 8 = -4x + 16

• x = 8

• x = 16

• x = 24

• x = 2

Solve:

• x = 13

• x = -13

• x = 12

• x = -15

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

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. Which equation could you use to see when the two companies would charge the same amount?

• 18x = 22x

• 3x + 15 = x + 21

• 15x + 3 = 21x + 1

• 3x + 15 + 21x = 1

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same. (Use an equation to help solve the problem)

• 3 hours

• 4 hours

• 1 hour

• 2 hours

8 - 3a + 12 = 2a

• a = 4

• a = 1

• a = 3

• a = 5

Solve for x

• x = 4

• x = 1

• 2x = 4

• x = 2

Write the equation for the model. (white square=1 rectangle=x red square = -1)

• 7=x+3

• 7=x+(-3)

• 7=-x+3

• -7=x-3

Solve the equation using the image. THE RECTANGLES ARE THE VARIABLES & THE SQUARES EQUAL ONE EACH.

• n = 14

• n = 6

• n = 7

• n = 2

If the triangle represents the variable and each circle equals one, is this model and equation in the image correct?

• Yes

• No, there needs to be 7 circles on the right side of the equal sign.

• No, there needs to be 4 circles on the right side of the equal sign.

• No, there needs to be a minus sign in the equation.