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 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 term across the equal sign, requiring manipulation to isolate the variable.

Front

Solve: 5x + 15 = 10x - 40

Back

x = 11

Front

Solve: -2x + 18 = 2x + 40

Back

x = -5.5

Front

Solve: 4x - 3 = 6x - 19

Back

x = 8

Front

Solve: 10 + 2n = 8n - 2n + 10

Back

n = 0

Front

Solve: 2(4x - 3) - 8 = 4 + 2x

Back

x = 3

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power, which can be combined by adding or subtracting their coefficients.

Front

What is the first step in solving a multi-step equation?

Back

The first step is often to simplify both sides of the equation by combining like terms and using the distributive property.