1. **State the problem:** Hazel inputs the same number $x$ into two different function machines, and the outputs are equal. We need to find the input number $x$. 2. **Write the functions:** - Top machine function: $$f(x) = 5(x - 8)$$ - Bottom machine function: $$g(x) = -3x + 8$$ 3. **Set the outputs equal:** Since the outputs are the same, we have: $$5(x - 8) = -3x + 8$$ 4. **Expand and simplify:** $$5x - 40 = -3x + 8$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$5x + 3x = 8 + 40$$ $$8x = 48$$ 6. **Solve for $x$:** $$x = \frac{48}{8}$$ $$x = 6$$ **Answer:** Hazel input the number $6$ into both machines to get the same output.