Let's solve the inequality first:

$-11 - 2d \geq 1$

Step 1: Add 11 to both sides

$-2d \geq 1 + 11$

$-2d \geq 12$

Step 2: Divide both sides by -2

When dividing by a negative number, remember to reverse the inequality sign:

$d \leq \frac{12}{-2}$

$d \leq -6$

So, the solution to the inequality is $d \leq -6$.

Interpreting the Graphs

On a number line, this solution is represented by an arrow starting at $-6$ with a filled circle (since the inequality is $\leq$) pointing to the left.

Without specific descriptions of the answer choices (A, B, C, D) like before, I can't point to the exact answer graphically. However, you should look for the graph that has a filled circle at $-6$ and an arrow pointing to the left.

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Would you like further details or have any questions?

Here are some related questions:

1. How would the graph change if the inequality was $d < -6$?
2. What if the inequality was $d \geq -6$? How would the graph look?
3. How do you represent the inequality $d > -6$ on a number line?
4. Can you explain why the inequality sign flips when dividing by a negative number?
5. What happens to the solution if the original inequality was $-11 + 2d \geq 1$ instead?

Tip: Always keep in mind to reverse the inequality sign when dividing or multiplying both sides by a negative number!