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 expressions on both the left and right sides of the equation, requiring manipulation to isolate the variable.

Front

How do you solve the equation: -8x - 8 + 3(x - 2) = -3x + 2?

Back

First, distribute the 3: -8x - 8 + 3x - 6 = -3x + 2. Combine like terms: -5x - 14 = -3x + 2. Add 3x to both sides: -2x - 14 = 2. Add 14 to both sides: -2x = 16. Divide by -2: x = -8.

Front

What is the solution to the equation: 10 + 2n = 8n - 2n + 10?

Back

Combine like terms on the right: 10 + 2n = 6n + 10. Subtract 10 from both sides: 2n = 6n. Subtract 6n from both sides: -4n = 0. Divide by -4: n = 0.

Front

How do you solve the equation: 8v - 4(v + 8) = 8?

Back

Distribute -4: 8v - 4v - 32 = 8. Combine like terms: 4v - 32 = 8. Add 32 to both sides: 4v = 40. Divide by 4: v = 10.

Front

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

Back

Distribute -2: 5y + 34 = 14y - 2. Subtract 5y from both sides: 34 = 9y - 2. Add 2 to both sides: 36 = 9y. Divide by 9: y = 4.

Front

How do you solve the equation: 4x - 3 = 6x - 19?

Back

Add 3 to both sides: 4x = 6x - 16. Subtract 6x from both sides: -2x = -16. Divide by -2: x = 8.

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 two or more terms inside a set of parentheses.

Front

What are like terms?

Back

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

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side of the equation by itself, making it easier to solve.