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

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to move all terms containing the variable to one side of the equation and constant terms to the other side.

Front

What is the first step in solving the equation 3(a + 22) = 12a + 30?

Back

The first step is to distribute the 3 on the left side, resulting in 3a + 66 = 12a + 30.

Front

What is the solution to the equation 5x - 14 = 8x + 4?

Back

The solution is x = -6.

Front

How do you check if your solution to an equation is correct?

Back

To check if your solution is correct, substitute the value back into the original equation and verify if both sides are equal.

Front

What is the importance of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve for the variable.

Front

What does it mean to 'move' a term from one side of the equation to the other?

Back

Moving a term involves performing an operation (like addition or subtraction) to both sides of the equation to maintain equality while isolating the variable.

Front

Solve for x: 4(1-x) + 3x = -2x - 2

Back

x = -6.

Front

What is the solution to the equation f - 4 = 6f + 26?

Back

The solution is f = -6.