Solving Multistep Equations

Front

What is a multistep equation?

Back

A multistep 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, you perform inverse operations to move all terms involving the variable to one side of the equation and constant terms to the other 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 solve the equation 4 - 2(x - 3) = 24?

Back

First, distribute -2: 4 - 2x + 6 = 24. Then combine like terms: 10 - 2x = 24. Subtract 10 from both sides: -2x = 14. Finally, divide by -2: x = -7.

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

How do you check your solution for an equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is the first step in solving the equation 96 = 6(k + 8)?

Back

The first step is to divide both sides by 6 to isolate the term with the variable: k + 8 = 16.

Front

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

Back

First, simplify both sides: 2x + 4 = 8x + 4. Then, subtract 4 from both sides: 2x = 8x. Finally, subtract 2x from both sides: 0 = 6x, leading to x = 0.

Front

What is an inverse operation?

Back

An inverse operation is an operation that reverses the effect of another operation, such as addition and subtraction or multiplication and division.

Front

What is the importance of maintaining balance in an equation?

Back

Maintaining balance in an equation means that whatever operation you perform on one side must also be performed on the other side to keep the equation true.