To determine which values are solutions to the inequality $4 \leq -7 + x$, we need to solve for $x$.

Steps to Solve the Inequality:

1. Start with the given inequality: $4 \leq -7 + x$

2. Add 7 to both sides to isolate $x$: $4 + 7 \leq x$

3. Simplify the left side: $11 \leq x$

This can also be written as: $x \geq 11$

Conclusion:

The solution to the inequality is $x \geq 11$.

Therefore, any value of $x$ that is 11 or greater will satisfy the inequality.

If you have specific values in mind that you'd like to test, feel free to share them! If not, this solution should clarify the range of values that satisfy the inequality.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How would the solution change if the inequality were $4 < -7 + x$ instead?
2. What happens if the inequality is flipped to $4 \geq -7 + x$?
3. Can you solve a similar inequality, such as $2 \leq 5 - x$?
4. How would the solution change if there were a coefficient in front of $x$?
5. How does solving inequalities differ from solving equations?

Tip: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.