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 operations such as 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 manipulation to combine like terms and solve for the variable.

Front

What is the first step in solving the equation 4(2a + 3) = −3(a − 1) + 31?

Back

The first step is to distribute the 4 and -3 to the terms inside the parentheses.

Front

What is the solution to the equation 6x + 5 = 10 + 5x?

Back

The solution is x = 5.

Front

What does it mean to 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 purpose of distributing in an equation?

Back

Distributing is used to eliminate parentheses by multiplying the term outside the parentheses by each term inside.

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 checking your solution in an equation?

Back

Checking your solution ensures that the value satisfies the original equation, confirming it is correct.

Front

What is the solution to the equation 12k + 15 = 35 + 2k?

Back

The solution is k = 2.