To solve the inequality $2 - x \leq 5$, follow these steps:

1. Subtract 2 from both sides to isolate the term involving $x$: $2 - x - 2 \leq 5 - 2$ This simplifies to: $-x \leq 3$

2. Multiply both sides by $-1$ to solve for $x$. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign: $x \geq -3$

So, the solution to the inequality is: $x \geq -3$

Would you like details or have any questions? Here are 5 related questions you might find helpful:

1. How would the solution change if the inequality was $2 - x \geq 5$?
2. What is the solution set for $3x + 4 < 2x + 10$?
3. How do you solve a compound inequality like $-2 \leq 3x - 1 < 5$?
4. Can you graph the solution $x \geq -3$ on a number line?
5. How do you solve inequalities involving absolute values?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.