Solving Equations with variables on both sides

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power, allowing them to be combined.

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to isolate the variable by moving all terms containing the variable to one side of the equation.

Front

How do you combine like terms?

Back

You combine like terms by adding or subtracting their coefficients while keeping the variable part the same.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has all real numbers as a solution?

Back

An equation has all real numbers as a solution if any value for the variable makes the equation true.

Front

How do you check if your solution to an equation is correct?

Back

You check your solution by substituting the value back into the original equation to see if both sides are equal.

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 each term inside a parenthesis.

Front

What is the purpose of isolating the variable?

Back

Isolating the variable helps to simplify the equation and makes it easier to solve for the variable.