1. **State the problem:** Chris inputs the same number $x$ into two function machines. The first machine outputs $-9 \times 3 \times x$, and the second machine outputs $-3 \times x + 15$. We need to find the value of $x$ such that both outputs are equal. 2. **Write the expressions for the outputs:** - First machine output: $$-9 \times 3 \times x = -27x$$ - Second machine output: $$-3x + 15$$ 3. **Set the outputs equal to each other:** $$-27x = -3x + 15$$ 4. **Solve for $x$:** Add $3x$ to both sides: $$-27x + 3x = 15$$ $$-24x = 15$$ Divide both sides by $-24$: $$x = \frac{15}{\cancel{-24}} \cancel{-1} = -\frac{15}{24}$$ Simplify the fraction by dividing numerator and denominator by 3: $$x = -\frac{5}{8}$$ 5. **Final answer:** The number Chris input is $\boxed{-\frac{5}{8}}$. This means when $x = -\frac{5}{8}$, both machines produce the same output.