Let's break this down step by step to solve for $x$.

The given equation is:

$x = \left[ \left( 115.0\% \times 3.50 \right) - \left( \frac{0.4235}{94.9\%} \right) - \left( \frac{3.25}{94.9\% \times 98\%} \right) \right] \times 50\%$

Step 1: Convert percentages to decimals

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

So the equation becomes:

$x = \left[ \left( 1.15 \times 3.50 \right) - \left( \frac{0.4235}{0.949} \right) - \left( \frac{3.25}{0.949 \times 0.98} \right) \right] \times 0.50$

Step 2: Simplify each term

1. $1.15 \times 3.50 = 4.025$
2. $\frac{0.4235}{0.949} = 0.4453$ (rounded to 4 decimal places)
3. $\frac{3.25}{0.949 \times 0.98} = \frac{3.25}{0.93002} = 3.4957$ (rounded to 4 decimal places)

Step 3: Plug these values back into the equation

$x = \left[ 4.025 - 0.4453 - 3.4957 \right] \times 0.50$

Step 4: Calculate inside the brackets

$4.025 - 0.4453 - 3.4957 = 0.084$

Step 5: Multiply by 50%

$x = 0.084 \times 0.50 = 0.042$

Final Answer:

$x = 0.042$

If you need further details or have any questions, feel free to ask!

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Related questions to explore:

1. How do you handle rounding when working with decimals in equations?
2. Why is it important to convert percentages into decimals before doing calculations?
3. What happens if you multiply the percentages before converting to decimals?
4. How would the result change if you used different rounding conventions?
5. Can you explain why 50% is applied at the end of this equation?

Tip: Always convert percentages to decimals before performing operations to avoid errors.