The expression you've given, `42 > h/4 + 43`, represents an inequality. Let's solve for the variable \( h \).

### Step-by-Step Solution

1. **Rewrite the inequality:**

   \[
   42 > \frac{h}{4} + 43
   \]

2. **Isolate the term with \( h \):**

   Subtract 43 from both sides:

   \[
   42 - 43 > \frac{h}{4}
   \]

   Simplifying the left side:

   \[
   -1 > \frac{h}{4}
   \]

3. **Solve for \( h \):**

   Multiply both sides by 4 to isolate \( h \):

   \[
   -1 \cdot 4 > h
   \]

   This simplifies to:

   \[
   -4 > h
   \]

   or equivalently:

   \[
   h < -4
   \]

### Conclusion

The solution to the inequality is:

\[
h < -4
\]

Would you like further details or have any questions?

### Related Questions to Explore:

1. What is the solution set for \( h > \frac{h}{4} + 15 \)?
2. How do you solve inequalities involving absolute values, like \( |h/4 + 43| > 42 \)?
3. How would the solution change if the inequality was \( 42 \geq \frac{h}{4} + 43 \)?
4. What happens if you multiply or divide an inequality by a negative number?
5. How can inequalities be represented on a number line?

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

Learn how to solve the inequality 42 > h/4 + 43 in this detailed step-by-step guide. Explore key algebraic concepts, such as solving for variables and handling inequalities. This solution is suitable for students in Grades 7-8.

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