Solving Equations Using the Distributive Property

What is the primary goal when solving equations?

• To apply the distributive property wherever possible

• To perform all operations within parentheses first

• To isolate the variable on one side of the equation

• To eliminate all constants from the equation

What does the distributive property allow us to do?

• Subtract a number from each term within parentheses

• Multiply a number by each term within parentheses

• Divide a number by each term within parentheses

• Add a number to each term within parentheses

How do we eliminate parentheses in an equation?

• By isolating the parentheses on one side

• By applying the distributive property

• By dividing the terms inside

• By subtracting the terms inside from both sides

What is the first step in solving equations with parentheses?

• Draw a line down the equal sign

• Perform inverse operations

• Apply the distributive property

• Isolate the variable

What is the result of applying the distributive property to 2(4x - 1)?

• 8x - 2

• 6x - 1

• 8x - 1

• 2x - 1

What is the inverse operation of multiplication when solving for a variable?

• Division

• Addition

• Subtraction

• Multiplication

After applying the distributive property, what should you do next?

• Repeat the distributive property

• Start performing inverse operations

• Check the solution immediately

• Apply the distributive property again

What does isolating the variable help to determine?

• The degree of the equation

• The value of the variable that satisfies the equation

• The coefficient of the variable

• The total number of variables in the equation

How can we verify that the solution to an equation is correct?

• By confirming the solution does not involve any fractions

• By ensuring the solution eliminates all variables

• By substituting the solution back into the original equation

• By checking if the solution is a positive number

Why do we substitute the solution back into the original equation?

• To find additional solutions

• To ensure the solution is accurate

• To simplify the equation further

• To demonstrate the distributive property