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. It often involves combining like terms, using the distributive property, and isolating the variable.

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 in more than one location in the equation, requiring manipulation to isolate the variable.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a set of parentheses.

Front

How do you combine like terms?

Back

To combine like terms, you add or subtract the coefficients of terms that have the same variable raised to the same power.

Front

What is the first step in solving the equation 5y + 34 = -2(-7y + 1)?

Back

The first step is to apply the distributive property to the right side of the equation, resulting in 5y + 34 = 14y - 2.

Front

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

Back

The solution is y = 4.

Front

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

Back

The first step is to distribute the 3 on the left side, resulting in -8x - 8 + 3x - 6 = -3x + 2.

Front

What is the solution to the equation -8x - 8 + 3(x - 2) = -3x + 2?

Back

The solution is x = -8.

Front

What does it mean to isolate the variable?

Back

Isolating the variable means manipulating the equation so that the variable is on one side of the equation by itself.

Front

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

Back

The solution is x = 9.