Write, Model, Solve 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 (often 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, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one 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 a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one and graphs as a straight line.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they yield the same results for the variable.

Front

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

Back

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

Front

What is the importance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides have the same value, which is fundamental to solving equations.