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*?

I., 5, II., 11, III., 4

I.5II.11III.4

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.

Explore how to find solutions to the inequality 4 ≤ -7 + x with a detailed step-by-step explanation. Learn about inequalities in algebra and how to determine which values satisfy them. Suitable for students in Grades 7-9.

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