Hanger Diagrams and Equations

Front

What is a hanger diagram?

Back

A visual representation used to illustrate the balance of weights on a hanger, often used in algebra to set up equations.

Front

How do you write an equation from a hanger diagram?

Back

Identify the weights on each side of the hanger and set them equal to each other to form an equation.

Front

What does the equation 3x + 15 = x + 30 represent in a hanger diagram?

Back

It represents a scenario where three weights of 'x' ounces plus 15 ounces balance with one weight of 'x' ounces plus 30 ounces.

Front

What is the first step in solving the equation 3x + 15 = x + 30?

Back

Subtract 'x' from both sides to simplify the equation.

Front

What is the solution to the equation 3x + 15 = x + 30?

Back

x = 7.5 ounces.

Front

What does the equation 2(x + 3y) + 2z = 2z + 4 + 2y represent?

Back

It represents a balance of weights where the left side equals the right side, showing how to distribute and combine terms.

Front

How do you simplify the equation 2(x + 3y) + 2z = 2z + 4 + 2y?

Back

Distribute the 2 on the left side to get 2x + 6y + 2z = 2z + 4 + 2y.

Front

What is the significance of the equation x + 3y = 2x + y?

Back

It shows a relationship between the variables x and y, indicating how they balance in the context of a hanger diagram.

Front

What is the process of matching steps in solving an equation?

Back

Identify the operations performed on both sides of the equation and match them to their corresponding steps.

Front

What does it mean if an equation is balanced?

Back

It means that the values on both sides of the equation are equal, representing a state of equilibrium.