Modeling/Solving Equations

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 is a variable in mathematics?

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 isolating the variable in an equation?

Back

Isolating the variable helps to find its value by getting it alone on one side of the equation.

Front

What is the first step in solving the equation 7w + 5 = 3w - 15?

Back

The first step is to move all terms involving the variable to one side and constant terms to the other side.

Front

How do 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 solution to the equation 10x + 9 = 4x - 9?

Back

x = -3.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.

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 set of parentheses.

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.