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

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

Back

Having variables on both sides of an equation means that the variable appears on both the left and right sides of the equation, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in a multi-step equation?

Back

To isolate a variable, you perform inverse operations to move all terms containing the variable to one side of the equation and constant terms to the other side.

Front

What is the first step in solving the equation 39 - 3b = -7(8b + 2)?

Back

The first step is to distribute -7 to both terms inside the parentheses on the right side of the equation.

Front

What is the solution to the equation 39 - 3b = -7(8b + 2)?

Back

The solution is b = -1.

Front

What does it mean to distribute in an equation?

Back

Distributing means to multiply a term outside the parentheses by each term inside the parentheses.

Front

How do you solve the equation 7(3n + 8) = 7(2n + 6)?

Back

First, divide both sides by 7, then simplify and isolate n.

Front

What is the solution to the equation 7(3n + 8) = 7(2n + 6)?

Back

The solution is n = -2.

Front

What is the importance of checking your solution in an equation?

Back

Checking your solution ensures that the value satisfies the original equation, confirming its correctness.

Front

What is the solution to the equation -6(2v + 4) = -8(v - 4)?

Back

The solution is v = -14.