1. **State the problem:** Solve the equation $$\frac{4}{x - 3} = 8$$ for $x$. 2. **Formula and rules:** To solve for $x$, we will isolate $x$ by first eliminating the denominator. Multiply both sides of the equation by $(x - 3)$ to get rid of the fraction. 3. **Intermediate work:** $$\frac{4}{x - 3} = 8 \implies 4 = 8(x - 3)$$ 4. **Simplify the right side:** $$4 = 8x - 24$$ 5. **Isolate $x$:** Add 24 to both sides: $$4 + 24 = 8x$$ $$28 = 8x$$ 6. **Divide both sides by 8:** $$x = \frac{28}{8} = 3.5$$ 7. **Final answer:** $$x = 3.500$$ (to 4 significant figures) Note: The expression $$\frac{e^{x/3}}{2}$$ is given but not part of the equation to solve here.