Solving 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 mathematical expressions or equations.

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 and constant terms to the other.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

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

How do you combine like terms in an equation?

Back

Combine like terms by adding or subtracting the coefficients of terms that have the same variable raised to the same power.

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it can be written in the form ax + b = c, where a, b, and c are constants.

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 values for the variable.

Front

What is the solution to the equation 1/2(s-12)= 1/4(s+ 16)?

Back

s = 40.