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 (usually letters) that represent unknown values in an equation.

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 sides of the equality sign.

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.

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 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 parenthesis.

Front

How do you combine like terms in an equation?

Back

You combine like terms by adding or subtracting coefficients of the same variable.

Front

What is the solution to the equation -8x - 8 + 3(x - 2) = -3x + 2?

Back

x = -8.

Front

What is the solution to the equation 4(1 - x) + 3x = -2(x + 1)?

Back

x = -6.