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.

Learn how to solve the inequality −8x + 10 > −22 with a clear, step-by-step solution. This problem demonstrates key algebraic concepts, including inequalities and the rule for reversing inequality signs when dividing by negative numbers. Perfect for students in Grades 7-8.

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