Solving Equations: variables on both sides

Front

What is an equation with variables on both sides?

Back

An equation where the variable appears on both the left and right sides, requiring manipulation to isolate the variable.

Front

What is a T-chart and how is it used in solving equations?

Back

A T-chart is a tool used to organize values of variables and their corresponding outputs, helping to visualize the relationship between them.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean when an equation has 'All Real Numbers' as a solution?

Back

It means that any value for the variable satisfies the equation, indicating that the two sides are equivalent for all real numbers.

Front

What is the first step in solving the equation -2(2f-4)= -4(-f +2)?

Back

Distribute the constants on both sides of the equation to eliminate parentheses.

Front

What is the significance of checking your solution in an equation?

Back

Checking your solution ensures that the value satisfies the original equation, confirming its correctness.

Front

What does it mean to have a solution of '4' for the equation -2m+13=2m-3?

Back

It means that when m equals 4, both sides of the equation are equal, making it a valid solution.

Front

What is the process of combining like terms in an equation?

Back

Combining like terms involves adding or subtracting terms that have the same variable and exponent to simplify the equation.

Front

What is the role of coefficients in an equation?

Back

Coefficients are the numerical factors that multiply the variables, affecting the value of the variable when solving the equation.

Front

How do you handle equations that result in a false statement, like 0=5?

Back

A false statement indicates that there is no solution to the equation, meaning the original equation is inconsistent.