x Consider the sequence of steps to solve the equation: \( 3(x-4)+5 x=9 x-36 \) Given \( \Rightarrow 3(x-4)+5 x=9 x-36 \) Step \( 1 \Rightarrow 3 x-12+5 x=9 x-36 \) Step \( 2 \Rightarrow 3 x+5 x-12=9 x-36 \) Step \( 3 \Rightarrow 8 x-12=9 x-36 \) Step \( 4 \Rightarrow 8 x-8 x-12=9 x-8 x-36 \) Step \( 5 \Rightarrow 0-12=x-36 \) Step \( 6 \Rightarrow-12=x-36 \) Step \( 7 \Rightarrow-12+36=x-36+36 \) Step \( 8 \Rightarrow 24=x+0 \) Step \( 9 \Rightarrow 24=x \) Which property yields Step 7 ? A Additive Inverse Property A \( \quad \) Additive Identity Property A \( \quad \) A \( \quad \) Addition Property of Equality

The property that yields Step 7 is the Addition Property of Equality. This property states that if you add the same value to both sides of an equation, the two sides remain equal. In this case, adding 36 to both sides transforms the equation from \(-12 = x - 36\) to \(24 = x\), keeping the equality intact and moving towards solving for \(x\). Now, let's talk about the Additive Inverse Property! This nifty property states that for any number \(a\), there exists an additive inverse, which is \(-a\), such that \(a + (-a) = 0\). It’s like magic with numbers! In solving equations, recognizing when you can use the additive inverse helps simplify your work significantly. So, let’s put on our math wizard hats and embrace these cool properties!