Let's break down and simplify the expression step by step.

The equation is:

$x = \left[ \left( 115.0\% \times 5.00 \right) - \left( \frac{0.35}{94.9\%} \right) - \left( \frac{4.75}{94.9\% \times 98\%} \right) \right] \times 50\%$

Step 1: Convert percentages to decimals

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

Now the equation becomes:

$x = \left[ \left( 1.15 \times 5.00 \right) - \left( \frac{0.35}{0.949} \right) - \left( \frac{4.75}{0.949 \times 0.98} \right) \right] \times 0.50$

Step 2: Simplify the multiplication and division

• $1.15 \times 5.00 = 5.75$
• $\frac{0.35}{0.949} \approx 0.369$
• $\frac{4.75}{0.949 \times 0.98} = \frac{4.75}{0.93002} \approx 5.11$

Now the equation is:

$x = \left[ 5.75 - 0.369 - 5.11 \right] \times 0.50$

Step 3: Simplify inside the brackets

$5.75 - 0.369 - 5.11 = 0.271$

Step 4: Multiply by 50%

$x = 0.271 \times 0.50 = 0.1355$

So, the value of $x$ is approximately 0.136.

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Let me know if you'd like further details or have any questions about the steps. Here are 5 related questions you can explore:

1. What are the properties of percentages in algebraic equations?
2. How does the order of operations (PEMDAS) affect solving complex expressions like this?
3. Can we express percentages as fractions and how does this affect calculations?
4. What happens if we change the percentage values slightly (e.g., from 94.9% to 95%)?
5. How would this equation change if you had to solve for another variable, such as the percentage?

Tip: When dealing with percentages, always remember to convert them to decimals first before performing any operations.