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 Combining Like Terms? A Step \( 1 \Rightarrow 2 x-8+6 x=9 x-10 \) B Step \( 2 \Rightarrow 2 x+6 x-8=9 x-10 \) C Step \( 3 \Rightarrow 8 x-8=9 x-10 \)

To determine which step in solving the equation \( 2(x-4)+6 x=9 x-10 \) is justified by combining like terms, let's analyze each step: 1. **Step 1:** \( 2 x - 8 + 6 x = 9 x - 10 \) - In this step, the expression \( 2(x-4) \) is expanded to \( 2x - 8 \), and \( 6x \) is added. This step does not involve combining like terms; it is simply expanding and rearranging. 2. **Step 2:** \( 2 x + 6 x - 8 = 9 x - 10 \) - Here, \( 2x \) and \( 6x \) are combined to form \( 8x \). This is indeed combining like terms. 3. **Step 3:** \( 8 x - 8 = 9 x - 10 \) - In this step, there is no combining of like terms; it is just rewriting the equation. Based on this analysis, the step that is justified by combining like terms is: **B Step 2: \( 2 x + 6 x - 8 = 9 x - 10 \)**.