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 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, requiring manipulation to isolate the variable on one side.

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 set of parentheses.

Front

How do you combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

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 4(2a + 3) = -3(a - 1) + 31?

Back

The solution is a = 2.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the solution to the equation 4(1 - x) + 3x = -2x - 2?

Back

The solution is x = -6.

Front

What does it mean to check your solution in an equation?

Back

Checking your solution means substituting the value back into the original equation to verify that both sides are equal.

Front

What is the solution to the equation 5x - 4 + 2x = 3?

Back

The solution is x = 1.