1. Stating the problem: Solve the equation $$\frac{4x}{1} \div 2 = x + 7$$. 2. Understand the division by 2: Dividing by 2 is the same as multiplying by $\frac{1}{2}$, so rewrite the left side: $$\frac{4x}{1} \times \frac{1}{2} = x + 7$$ 3. Simplify the left side: $$\frac{4x}{1} \times \frac{1}{2} = \frac{4x \times 1}{1 \times 2} = \frac{4x}{2}$$ 4. Simplify the fraction by canceling common factors: $$\frac{\cancel{4}x}{\cancel{2}} = 2x$$ 5. Now the equation is: $$2x = x + 7$$ 6. Subtract $x$ from both sides to isolate $x$: $$2x - x = x + 7 - x$$ $$x = 7$$ 7. Final answer: $$x = 7$$