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Let's solve the inequality step by step.

We are given the inequality:

\[
-2y - 11 \geq 13
\]

### Step 1: Isolate the term with \( y \)
Start by adding 11 to both sides of the inequality to eliminate the constant term on the left-hand side:

\[
-2y - 11 + 11 \geq 13 + 11
\]

\[
-2y \geq 24
\]

### Step 2: Solve for \( y \)
Now, divide both sides of the inequality by \(-2\). Remember that when you divide or multiply an inequality by a negative number, you must flip the inequality sign:

\[
y \leq \frac{24}{-2}
\]

\[
y \leq -12
\]

### Final Answer:
The solution to the inequality is:

\[
y \leq -12
\]

Would you like further details on this, or do you have any questions?

Here are some additional related questions:

1. What happens if we multiply both sides of an inequality by a negative number?
2. How does solving an inequality differ from solving an equation?
3. Can you graph the solution \( y \leq -12 \) on a number line?
4. What if the original inequality was \( -2y - 11 > 13 \)? How would the solution change?
5. Can we check the solution by plugging \( y = -12 \) back into the original inequality?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the inequality -2y - 11 ≥ 13 with a detailed step-by-step solution. This problem covers key algebraic concepts such as isolating variables, basic inequality manipulation, and flipping the inequality sign when multiplying or dividing by a negative number. Suitable for students in Grades 7-9.

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