To analyze the given inequality $|x + 5| \geq 7$, we need to interpret what it means on the number line.

Steps to Solve:

1. Recall the definition of absolute value: |A| \geq B \implies A \leq -B \text{ or } A \geq B \quad \text{(for B \geq 0)}.

2. Here, $A = x + 5$ and $B = 7$. So: $x + 5 \leq -7 \quad \text{or} \quad x + 5 \geq 7.$

3. Solve each part:

   • $x + 5 \leq -7 \implies x \leq -12$,
   • $x + 5 \geq 7 \implies x \geq 2$.

Thus, the solution is: $x \leq -12 \quad \text{or} \quad x \geq 2.$

Interpretation:

This means $x$ is at least 7 units away from $-5$ on the number line, either in the negative direction ($x \leq -12$) or in the positive direction ($x \geq 2$).

Correct Answer:

"more than or exactly 7 units from -5."

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Would you like further explanation or have additional questions? Here are some related questions to consider:

1. How do we graph $|x + 5| \geq 7$ on the number line?
2. What is the difference between $|x + 5| \geq 7$ and $|x + 5| \leq 7$?
3. What are some real-world applications of absolute value inequalities?
4. How do we solve inequalities like $|x - c| > d$?
5. What changes if the inequality sign switches to $>$ or $<$?

Tip: Always visualize absolute value inequalities on the number line to better understand their solutions.