Let's determine whether each of the given values satisfies the inequality $4 \leq -7 + x$.

Recall the inequality:

$4 \leq -7 + x$ This simplifies to: $x \geq 11$

Now, let's check each value:

I. $x = 5$

Substitute $x = 5$ into the inequality: $4 \leq -7 + 5$ $4 \leq -2$ This is false, so $x = 5$ is not a solution.

II. $x = 11$

Substitute $x = 11$ into the inequality: $4 \leq -7 + 11$ $4 \leq 4$ This is true, so $x = 11$ is a solution.

III. $x = 4$

Substitute $x = 4$ into the inequality: $4 \leq -7 + 4$ $4 \leq -3$ This is false, so $x = 4$ is not a solution.

Conclusion:

The only value that satisfies the inequality $4 \leq -7 + x$ is II. $x = 11$.

Would you like more details or have any questions? Here are some related questions to explore further:

1. How would the solution change if the inequality were $4 < -7 + x$?
2. Can you solve a similar inequality, such as $3 \leq -5 + x$?
3. What happens if we flip the inequality to $4 \geq -7 + x$?
4. How does substituting different values of $x$ affect the truth of the inequality?
5. What would happen if there was a coefficient in front of $x$, like $4 \leq -7 + 2x$?

Tip: Always substitute values carefully into inequalities and simplify step by step to check if they hold true.