(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 4 ? A Subtraction Property of Equality A \( \quad \) B Commutative Property of Addition Ax C Addition Property of Equality C
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Mind Expander
In Step 4, we utilize the Subtraction Property of Equality. This property allows us to subtract the same amount from both sides of an equation, ensuring that the equality remains valid. In this case, we subtracted \(8x\) from both sides, simplifying our equation while maintaining its truth. Following the sequence, it’s crucial to avoid common mistakes like forgetting to apply operations to both sides of the equation or miscalculating during simplification. Always double-check each step! Carefully line up your terms to prevent any unexpected errors from sneaking into your solution. Happy solving!
