1. The problem states: "The sum of the opposite of a number $x$ and six is less than or equal to five."\n\n2. Let's translate the words into a mathematical inequality. "Opposite of a number $x$" means $-x$.\n\n3. "The sum of the opposite of $x$ and six" means $-x + 6$.\n\n4. "Is less than or equal to five" translates to $\leq 5$.\n\n5. Putting it all together, the inequality is: $$-x + 6 \leq 5$$\n\n6. To isolate $x$, subtract 6 from both sides: $$-x + 6 - 6 \leq 5 - 6$$\n\n7. Simplify: $$-x \leq -1$$\n\n8. Now, multiply both sides by $-1$ to solve for $x$. Remember, multiplying an inequality by a negative number reverses the inequality sign: $$\cancel{-1} \times -x \geq \cancel{-1} \times -1$$\n\n9. Simplify: $$x \geq 1$$\n\nFinal answer: $$x \geq 1$$