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 (like x, y, or f) that represent unknown values in mathematical expressions or equations.

Front

What is the goal when solving equations with variables on both sides?

Back

The goal is to isolate the variable on one side of the equation to find its value.

Front

What is the first step in solving an equation like f - 4 = 6f + 26?

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 combine like terms in an equation?

Back

You combine like terms by adding or subtracting coefficients of the same variable.

Front

What is the solution to the equation 3c + 5 = 23?

Back

c = 6.

Front

How do you check if your solution to an equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 7w + 5 = 3w - 15?

Back

w = -5.

Front

What does it mean to isolate a variable?

Back

To isolate a variable means to manipulate the equation so that the variable is alone on one side of the equation.