Multi-Step Equations 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 like addition, subtraction, multiplication, and division.

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

Back

It means that the variable appears on both sides of the equation, requiring you to combine like terms to solve for the variable.

Front

What is the first step in solving the equation 3(x + 1) - 5 = 5x - 2?

Back

The first step is to distribute the 3 to both terms inside the parentheses: 3x + 3 - 5 = 5x - 2.

Front

What is the solution to the equation 2x + 3(5x - 7) = 47?

Back

The solution is x = 4.

Front

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

Back

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

Front

What is the purpose of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve for the variable.

Front

What does the equation 7(1 - y) = -3(y - 2) represent?

Back

It represents a multi-step equation that can be solved for the variable y.

Front

What is the solution to the equation 3(a + 22) = 12a - 30?

Back

The solution is a = 4.

Front

What is the importance of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by terms inside parentheses, which is essential for simplifying equations.