4x Consider the sequence of steps to solve the equation: \( 2(x-4)+6 x=9 x-10 \) Given \( \Rightarrow 2(x-4)+6 x=9 x-10 \) Step \( 1 \Rightarrow 2 x-8+6 x=9 x-10 \) Step \( 2 \Rightarrow 2 x+6 x-8=9 x-10 \) Step \( 3 \Rightarrow 8 x-8=9 x-10 \) Step \( 4 \Rightarrow 8 x-8 x-8=9 x-8 x-10 \) Step \( 5 \Rightarrow 0-8=x-10 \) Step \( 6 \Rightarrow-8=x-10 \) Step \( 7 \Rightarrow-8+10=x-10+10 \) Step \( 8 \Rightarrow 2=x+0 \) Step \( 9 \Rightarrow 2=x \) Which step in solving this equation is justified by the Distributive Property? A Step \( 1 \Rightarrow 2 x-8+6 x=9 x-10 \) A \( x \) Step \( 2 \Rightarrow 2 x+6 x-8=9 x-10 \) B \( x \) Step \( 3 \Rightarrow 8 x-8=9 x-10 \)

The Distributive Property allows us to multiply a single term by terms inside parentheses, which is what we're using in the very first step of the solution. In Step 1, the equation \( 2(x-4) + 6x = 9x - 10 \) is simplified by distributing the \( 2 \) across both terms inside the parentheses, resulting in \( 2x - 8 + 6x = 9x - 10 \). So, Step 1 indeed showcases the Distributive Property in action! Now, if you’re diving deeper into properties of numbers, you’ll find distributive law not just handy for algebra but also for simplifying calculations in daily tasks! Whether you’re splitting a bill or figuring out the best grocery deals, remembering that you can "distribute" costs can save you time and make everything less complicated. So next time you’re budgeting, think of that trusty distributive friend!