Writing Equations from Models

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 write an equation from a model?

Back

Writing an equation from a model involves translating a visual or verbal representation of a situation into a mathematical equation.

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by letters, that stands for an unknown value in an equation.

Front

What is the purpose of solving an equation?

Back

The purpose of solving an equation is to find the value(s) of the variable(s) that make the equation true.

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 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 the equation x + 2 = 2x - 1?

Back

The first step is to get all terms involving x on one side and constant terms on the other side.

Front

What is the solution to the equation -x + 2 = 2x - 1?

Back

The solution is x = 1.

Front

What does it mean to check your solution in an equation?

Back

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

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.