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The problem is asking which inequality is **not equivalent** to the given inequality:

\[
-7 < x + a
\]

Let's simplify and analyze the choices:

1. **Original inequality:**
   \[
   -7 < x + a
   \]
   To isolate \(x\), subtract \(a\) from both sides:
   \[
   -7 - a < x
   \]
   This simplifies to:
   \[
   x > -7 - a
   \]
   (Note: when you swap sides of an inequality, you also change the direction of the inequality.)

Now, compare each option to see if they are equivalent:

### A. \(x > -7 + a\)
This differs from the original inequality \(x > -7 - a\), so **A is not equivalent**.

### B. \(-7 - x < a\)
Rearrange this to isolate \(x\):
\[
-x < a + 7
\]
Multiply through by \(-1\) (which reverses the inequality):
\[
x > -7 - a
\]
This matches the original inequality, so **B is equivalent**.

### C. \(-7 + a > x\)
Rearranging this gives:
\[
x < -7 + a
\]
This is the reverse of the original inequality, so **C is not equivalent**.

### D. \(0 > -7 - x - a\)
Rearrange this inequality:
\[
0 > -7 - a - x
\]
Add \(x\) to both sides:
\[
x > -7 - a
\]
This is the same as the original inequality, so **D is equivalent**.

### Conclusion:
The inequalities that are **not equivalent** are:

- **A** and **C**

Would you like further details or explanations?

Here are 5 related questions to consider:
1. How do you solve linear inequalities involving multiple terms?
2. What are the rules for reversing the direction of an inequality?
3. How does subtraction affect both sides of an inequality?
4. How can inequalities be represented graphically on a number line?
5. What methods can be used to check the solution of inequalities?

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

Which inequality is not equivalent to the inequality -7 < x + a, where a is a constant?

Explore how to determine which inequality is not equivalent to -7 < x + a. Understand inequality manipulation and key algebraic steps used to solve this problem. Ideal for students in Grades 8-10.

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