To solve the inequality $-8x + 10 > -22$, follow these steps:

1. Subtract 10 from both sides of the inequality: $-8x + 10 - 10 > -22 - 10$ Simplifying: $-8x > -32$

2. Divide both sides by $-8$. Remember, when you divide by a negative number, the inequality sign flips: $x < \frac{-32}{-8}$ Simplifying: $x < 4$

Thus, the solution is $x < 4$.

Would you like further details or have any questions? Here are 5 related questions to extend your understanding:

1. How do you solve $5x - 3 > 12$?
2. Can you solve $-3x + 7 \leq 4$?
3. What happens to the inequality when dividing by a negative number?
4. Solve $6x + 2 \geq 14$.
5. What are the key differences between solving equations and inequalities?

Tip: When solving inequalities, always remember to reverse the inequality sign if you multiply or divide by a negative number.