Let’s break down this equation step by step to solve for $x$:

The equation is:

$x = \left[ (115.0\% \times 4.00) - \left( \frac{0.35}{94.9\%} \right) - \left( \frac{3.75}{94.9\% \times 98\%} \right) \right] \times 50\%$

Step 1: Convert percentages to decimal form

• $115.0\% = 1.15$
• $94.9\% = 0.949$
• $98\% = 0.98$
• $50\% = 0.50$

Step 2: Apply the percentages

1. $115.0\% \times 4.00 = 1.15 \times 4.00 = 4.60$
2. $\frac{0.35}{94.9\%} = \frac{0.35}{0.949} \approx 0.369$
3. $\frac{3.75}{94.9\% \times 98\%} = \frac{3.75}{0.949 \times 0.98} = \frac{3.75}{0.93002} \approx 4.03$

Step 3: Substitute these values back into the equation

$x = \left[ 4.60 - 0.369 - 4.03 \right] \times 0.50$

$x = \left[ 4.60 - 4.399 \right] \times 0.50$

$x = 0.201 \times 0.50$

Step 4: Final result

$x = 0.1005$

So, $x \approx 0.1005$.

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Would you like more details on how to approach such equations or have any other questions on this topic?

Here are some related questions:

1. How do you handle more complex equations involving multiple percentages?
2. What does it mean to convert percentages to decimal form, and why is it important?
3. Can this method be applied to equations involving other operations like multiplication or division?
4. How do you handle situations where percentages are in the denominator of a fraction?
5. What would happen if we changed the 50% factor to another percentage?

Tip: When dealing with percentages in equations, always remember to convert them to their decimal equivalents (e.g., $115\% = 1.15$) before performing any calculations!