1. The problem is to solve the equation $7 + x = \frac{1}{2}(4x - 2)$ and identify the step where a mistake occurs. 2. Start with the original equation: $$7 + x = \frac{1}{2}(4x - 2)$$ 3. Step 1 shows the original equation correctly. 4. Step 2 multiplies the right side: $$\frac{1}{2} \times 4x = 2x \quad \text{and} \quad \frac{1}{2} \times (-2) = -1$$ So, $$7 + x = 2x - 1$$ This step is correct. 5. Step 3 subtracts $x$ and adds $1$ to both sides: $$7 + x = 2x - 1$$ Subtract $x$: $$7 = 2x - 1 - x$$ Simplify: $$7 = x - 1$$ Add $1$: $$7 + 1 = x$$ $$8 = x$$ But Step 3 shows: $$6 = 3x$$ which is incorrect. 6. Therefore, the mistake is in Step 3. 7. The correct solution is: $$x = 8$$