Solving and Writing 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 inverse operations to get the variable alone on one side of the equation.

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 variable terms 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.

Front

What does it mean to write an equation from a word problem?

Back

It means to translate the situation described in the problem into a mathematical equation using variables.

Front

How do you determine the cost of playing games at two different locations?

Back

You set up equations based on the rental fees and per-game costs, then solve for the number of games where costs are equal.

Front

What is the significance of the solution to an equation?

Back

The solution represents the value of the variable that satisfies the equation, often answering a real-world question.