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The inequality provided is:

\[
-4(-8 + x) > 40
\]

### Step-by-Step Solution:

1. **Distribute the -4**:
   \[
   -4(-8 + x) = (-4)(-8) + (-4)(x) = 32 - 4x
   \]
   So, the inequality becomes:
   \[
   32 - 4x > 40
   \]

2. **Isolate the variable term (-4x)**:
   Subtract 32 from both sides:
   \[
   32 - 4x - 32 > 40 - 32
   \]
   Simplifying:
   \[
   -4x > 8
   \]

3. **Solve for \(x\)**:
   Divide both sides by -4. **Important:** When you divide or multiply by a negative number in an inequality, you must **flip the inequality sign**:
   \[
   x < \frac{8}{-4}
   \]
   Simplifying:
   \[
   x < -2
   \]

### Final Answer:
\[
x < -2
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How does multiplying or dividing an inequality by a negative number affect the inequality sign?
2. How would the solution change if the inequality were \( \geq \) instead of \( > \)?
3. What would happen if the inequality had an additional constant term on the left side?
4. Can this inequality be graphed on a number line? How would the solution look visually?
5. How does solving inequalities differ from solving regular equations?

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

Solve for x in the inequality: -4(-8 + x) > 40

This problem explains how to solve the linear inequality -4(-8 + x) > 40, focusing on key algebra concepts such as the distributive property and the rules for inequalities when multiplying or dividing by negative numbers. The step-by-step solution is ideal for students in Grades 7-9.

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