1. **State the problem:** We need to find which values of $x$ satisfy the inequality $$86 \leq 11x.$$ 2. **Write the formula and rules:** To solve for $x$, we divide both sides of the inequality by 11. Since 11 is positive, the inequality direction remains the same. 3. **Solve the inequality:** $$86 \leq 11x$$ Divide both sides by 11: $$\frac{86}{\cancel{11}} \leq \frac{11x}{\cancel{11}}$$ Simplifies to: $$\frac{86}{11} \leq x$$ 4. **Evaluate the fraction:** $$\frac{86}{11} = 7.8181...$$ 5. **Interpret the solution:** The inequality means $x$ must be greater than or equal to approximately 7.8181. 6. **Check each given value:** - $x=12$: $12 \geq 7.8181$ (True) - $x=9$: $9 \geq 7.8181$ (True) - $x=5$: $5 \geq 7.8181$ (False) - $x=1$: $1 \geq 7.8181$ (False) **Final answer:** The values $x=12$ and $x=9$ satisfy the inequality. The values $x=5$ and $x=1$ do not. Note: The user's checked boxes for $x=12$, $x=9$, and $x=1$ include one incorrect choice ($x=1$).