We are given the equation:

$2 - 48 = (H - 48) \left(\frac{5,101 - 14,930}{5,101}\right)$

Let's solve for $H$.

Step 1: Simplify the expression inside the parentheses.

$\frac{5,101 - 14,930}{5,101} = \frac{-9,829}{5,101}$

Now, approximate the division: $\frac{-9,829}{5,101} \approx -1.926$

Step 2: Substitute the simplified expression back into the equation:

$2 - 48 = (H - 48)(-1.926)$ $-46 = (H - 48)(-1.926)$

Step 3: Solve for $H$.

Divide both sides by $-1.926$: $\frac{-46}{-1.926} = H - 48$ $23.88 \approx H - 48$

Step 4: Add 48 to both sides to isolate $H$:

$H \approx 23.88 + 48$ $H \approx 71.88$

Thus, $H \approx 71.88$.

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Do you want more details on any step? Let me know if you have any questions!

Related Questions:

1. What is the exact value if we calculate the decimal more precisely?
2. How can this be solved graphically?
3. What happens if we change the denominator to a different value?
4. How would this be different if the expression was squared?
5. How can you check if the solution is correct by substituting $H$ back into the original equation?

Tip: Always double-check your arithmetic operations, especially when dealing with negative values.