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 mathematical expressions or equations.

Front

What is the purpose of writing an equation from a word problem?

Back

Writing an equation from a word problem helps to translate the situation into a mathematical form that can be solved.

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 all other terms on the opposite side.

Front

What is the first step in solving the equation 400 + 75x = 1,000 - 25x?

Back

The first step is to combine like terms by adding 25x to both sides to eliminate the variable from the right side.

Front

What does it mean for two expressions to be equal in an equation?

Back

It means that the values of the expressions are the same for the values of the variables that satisfy the equation.

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

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 significance of the coefficients in an equation?

Back

Coefficients are the numerical factors that multiply the variables in an equation, affecting the slope and position of the line when graphed.