Ask a New Question
Menu

Eric, Emily and Noah were all solving the problem 3(x+2)-9-2+3

. Eric said the first step should be the Distributive Property, Emily said the first step should be the Addition Property of Equality, and Noah said the first step should be the Subtraction Property of Equality. Who was correct?

1 answer

To solve the expression \(3(x + 2) - 9 - 2 + 3\), let's analyze what needs to be done first.

  1. Distributive Property: This involves distributing the \(3\) across the terms in the parentheses. This can be considered as the first step because to simplify \(3(x + 2)\), we would apply the distributive property: \[ 3(x + 2) = 3x + 6 \] So, if we follow Eric's suggestion first, we would proceed to: \[ 3x + 6 - 9 - 2 + 3 \]

  2. Addition Property of Equality: This property states that if you add the same value to both sides of an equation, the equality remains true. However, we are simplifying an expression here, not solving an equation where this property would apply directly.

  3. Subtraction Property of Equality: Similar to the Addition Property, this property applies to equations when subtracting the same value from both sides. Again, this is not applicable while simplifying an expression without an equation.

Therefore, the correct first step in solving the problem \(3(x + 2) - 9 - 2 + 3\) is to apply the Distributive Property, as Eric suggested.