Equivalent equations and moves

Front

What is an equivalent equation?

Back

An equivalent equation is an equation that has the same solution as another equation, meaning both equations represent the same relationship.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side of the equation and all other terms are on the opposite side.

Front

What is the purpose of balancing an equation?

Back

Balancing an equation ensures that both sides of the equation remain equal after performing operations, maintaining the equality.

Front

What is the first step in solving an equation?

Back

The first step in solving an equation is to simplify both sides of the equation, if possible, by combining like terms and using the distributive property.

Front

What does it mean to add the same number to both sides of an equation?

Back

Adding the same number to both sides of an equation keeps the equation balanced and does not change the solution.

Front

What is the result of multiplying both sides of an equation by zero?

Back

Multiplying both sides of an equation by zero results in both sides being equal to zero, which can lead to loss of information about the original equation.

Front

What is the significance of the coefficient in an equation?

Back

The coefficient is the numerical factor in front of a variable, indicating how many times the variable is multiplied.

Front

How do you check if two equations are equivalent?

Back

To check if two equations are equivalent, solve both equations for the variable and compare the solutions.