The inequality given is:

\[
-2x - 1 \geq 7
\]

### Solution steps:

1. **Add 1 to both sides** to eliminate the constant term on the left:
   \[
   -2x - 1 + 1 \geq 7 + 1
   \]
   \[
   -2x \geq 8
   \]

2. **Divide both sides by -2**, but remember: when dividing by a negative number, **the inequality sign must flip**:
   \[
   x \leq \frac{8}{-2}
   \]
   \[
   x \leq -4
   \]

### Final answer:
\[
x \leq -4
\]

Would you like any further details or clarification?

Here are 5 related questions you might find useful:

1. How would you solve an inequality with fractions?
2. What changes when dividing or multiplying by negative numbers in inequalities?
3. How do you graph solutions to inequalities on a number line?
4. Can inequalities have multiple steps and involve distributing terms?
5. What is the difference between "strict" inequalities and "non-strict" inequalities?

**Tip:** Always flip the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve the linear inequality −2x−1≥7 with a clear, step-by-step solution. This problem involves key algebraic concepts such as inequality manipulation and flipping the inequality sign when dividing by negative numbers. Suitable for students in Grades 6-8.

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