Let's break down the expression step by step to find the value of $x$:

$x = \left[ \left( 115.0\% \times 4.50 \right) - \left( \frac{0.35}{94.9\%} \right) - \left( \frac{4.25}{94.9\% \times 98\%} \right) \right] \times 50\%$

Step 1: Convert percentages to decimals

• $115.0\% = 1.15$
• $94.9\% = 0.949$
• $98\% = 0.98$
• $50\% = 0.5$

So the expression becomes:

$x = \left[ (1.15 \times 4.50) - \left( \frac{0.35}{0.949} \right) - \left( \frac{4.25}{0.949 \times 0.98} \right) \right] \times 0.5$

Step 2: Evaluate each part

1. $1.15 \times 4.50 = 5.175$
2. $\frac{0.35}{0.949} \approx 0.369$
3. $\frac{4.25}{0.949 \times 0.98} = \frac{4.25}{0.93002} \approx 4.57$

Step 3: Combine the results

Now, substitute these values back into the equation:

$x = \left[ 5.175 - 0.369 - 4.57 \right] \times 0.5$

$x = \left[ 5.175 - 4.939 \right] \times 0.5$

$x = 0.236 \times 0.5$

$x = 0.118$

Final Answer:

$x \approx 0.118$

If you have any more questions or want further clarification, feel free to ask!

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Here are some related questions to explore:

1. What happens to the value of $x$ if the percentage values change slightly?
2. How would you approach solving this if the percentages were given in fractional form instead of decimals?
3. What is the impact of changing the denominator values in each fraction on the final result?
4. How can you apply similar methods to more complex financial calculations?
5. Can you solve this equation using a different order of operations?

Tip: When dealing with percentages in equations, always convert them into decimal form by dividing by 100 to simplify calculations.