Which of the following values are solutions to the inequality 4, is less than or equal to, minus, 7, plus, x, question mark4≤−7+x

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.

Explore how to solve the inequality 4 ≤ -7 + x step-by-step with detailed explanations. Understand the range of values for x that satisfy the inequality. Suitable for students in Grades 7-9 studying algebra and inequalities.

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