Solving Multi-Step Equations with Variables on Both Sides

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, and division.

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 does it mean to have variables on both sides of an equation?

Back

Having variables on both sides means that the variable appears in expressions on both sides of the equal sign, requiring manipulation to solve.

Front

What is the first step in solving the equation 3(2k + 3) = -(-7k + 1)?

Back

The first step is to simplify both sides of the equation by distributing the numbers outside the parentheses.

Front

What is the solution to the equation 3(2k + 3) = -(-7k + 1)?

Back

The solution is k = 10.

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 4n - 2 = -2 + 8n?

Back

The solution is n = 0.

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 the solution to the equation n + 1 - 3n = 9 - n?

Back

The solution is n = -8.

Front

What is the importance of keeping the equation balanced when solving?

Back

Keeping the equation balanced ensures that whatever operation you perform on one side must also be performed on the other side to maintain equality.