To solve the inequality:

\[
-2x + 1 > -11
\]

### Step-by-Step Solution

1. **Subtract 1 from both sides** to isolate the term with \(x\):
   \[
   -2x > -11 - 1
   \]
   \[
   -2x > -12
   \]

2. **Divide both sides by -2** to solve for \(x\), remembering to **reverse the inequality sign** when dividing by a negative number:
   \[
   x < \frac{-12}{-2}
   \]
   \[
   x < 6
   \]

### Final Answer:
\[
x < 6
\]

Would you like more details or have any questions?

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1. How do you graph inequalities on a number line?
2. What happens if you multiply or divide by a negative in an inequality?
3. How do you check if a solution satisfies an inequality?
4. Can inequalities have solutions represented by intervals?
5. How do absolute values affect inequalities?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number!

Understand how to solve the inequality -2x + 1 > -11 with a comprehensive, step-by-step solution. This problem demonstrates key algebraic concepts, including inequalities and the rule for reversing inequality signs when dividing by a negative. Suitable for students in Grades 7-9.

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