Question

Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.

A. + 7 = 12; x = 5
B. x = 5 + 7; x = 12
C. x + 5 = 7; x = 2
D. x + 7 = 5; x = -2

Answer 1

C: x + 5 = 7; x = 2

Explanation:

Refer to the given model. On the left-hand side of the balance beam, there are five circles and one square. On the right-hand side of the balance beam, there are seven circles. The balance beam is evenly distributed, so the value on the left-hand side of the balance beam must be the same as the value on the right-hand side of the balance beam.

The square stands for an unknown quantity. In algebra, variables are used to represent unknown quantities, so x will represent the value of the square.

The model shows that the value of x plus five circles is the same as seven circles. Replacing the word "plus" with a plus sign and replacing "is the same as" with an equal sign gives the equation x + 5 = 7.

To solve the equation, subtract 5 from both sides of the equation to isolate x.

Thus, the solution to the equation is x = 2.

Answer 2

C

Explanation:

We can notice that the balance beam has in one side 7 balls and in the other one 5 balls and a square

The balance beam is balenced

Let x be the square mass

• x+5 = 7 substract five from each side
• x+5-5 = 7-5
• x = 2

The solution is 2

C fits perfectly what we prooved