1. **State the problem:** We have a function machine where an unknown input $x$ is first multiplied by $-7$, then $3$ is added, resulting in an output of $-11$. 2. **Write the equation:** The function can be expressed as $$-7x + 3 = -11$$ 3. **Solve for $x$:** - Subtract 3 from both sides: $$-7x = -11 - 3$$ $$-7x = -14$$ - Divide both sides by $-7$: $$x = \frac{-14}{-7}$$ $$x = 2$$ 4. **Interpretation:** The input to the function machine is $2$ to get the output $-11$ after multiplying by $-7$ and adding $3$. **Final answer:** $x = 2$