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!