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 variables in an equation?

Back

Variables are symbols (like x or y) that represent unknown values in mathematical expressions or equations.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the variable appears in expressions on both the left and right sides of the equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform operations to get the variable on one side of the equation and the constants on the other side.

Front

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

Back

The first step is to simplify both sides of the equation if necessary, and then move all terms containing the variable to one side.

Front

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

Back

Combining like terms simplifies the equation, making it easier to solve for the variable.

Front

What does it mean to check your solution?

Back

Checking your solution means substituting the found value back into the original equation to verify that both sides are equal.

Front

What is the solution to the equation 5x - 21 = 2x - 6?

Back

The solution is x = 5.

Front

What is the solution to the equation -8 - x = x - 4x?

Back

The solution is x = 4.