1. The problem is to solve the equation for $x$ given that each person gets $\frac{1}{4}$ of a gallon of lemonade. 2. We are given four possible equations: - $8x = \frac{1}{4}$ - $x + 8 = \frac{1}{4}$ - $\frac{x}{8} = \frac{1}{4}$ - $x - 8 = \frac{1}{4}$ 3. We will solve the first equation $8x = \frac{1}{4}$ step-by-step. 4. To isolate $x$, divide both sides of the equation by 8: $$8x = \frac{1}{4}$$ $$\cancel{8}x = \frac{1}{4} \div \cancel{8}$$ This simplifies to: $$x = \frac{1}{4} \times \frac{1}{8}$$ 5. Multiply the fractions: $$x = \frac{1 \times 1}{4 \times 8} = \frac{1}{32}$$ 6. Therefore, the solution to the equation $8x = \frac{1}{4}$ is: $$\boxed{x = \frac{1}{32}}$$ This means each person gets $\frac{1}{32}$ gallons of lemonade if the total is divided such that $8x = \frac{1}{4}$. Note: The other equations are not solved here as per instructions to solve only the first problem.