1. **State the problem:** Anna inputs the same number $x$ into two different function machines, and the outputs are equal. We need to find the value of $x$. 2. **Write the expressions for each machine:** - First machine: Input $x$ goes through subtract 9, then multiply by 5. So output is $$5(x - 9)$$. - Second machine: Input $x$ goes through multiply by -3, then add 11. So output is $$-3x + 11$$. 3. **Set the outputs equal:** $$5(x - 9) = -3x + 11$$ 4. **Expand and simplify:** $$5x - 45 = -3x + 11$$ 5. **Collect like terms:** Add $3x$ to both sides: $$5x + 3x - 45 = 11$$ $$8x - 45 = 11$$ Add $45$ to both sides: $$8x = 11 + 45$$ $$8x = 56$$ 6. **Solve for $x$:** Divide both sides by 8: $$x = \frac{56}{8} = 7$$ **Final answer:** Anna input the number $7$ into both machines to get the same output.