Solve the equation for \( x \):

\[
\frac{(4 - 3.5 \cdot (2 \frac{1}{7} - 1 \frac{1}{5})) \div 0.16}{x} = \frac{3 \frac{2}{7} - \frac{3}{14} \div \frac{1}{6}}{41 \frac{23}{84} - 40 \frac{49}{60}}
\]

The problem involves solving an advanced mathematical equation. It requires multiple steps of algebraic simplification, including arithmetic operations on fractions, applying order of operations, and possibly, using advanced methods like the quadratic formula.

Explanation:

The subject of this question is Mathematics. This problem involves solving an algebraic equation. To solve this equation, first simplify each side of the equation, and then find the value for the variable 'x'.

However, some additional information given in the problem does not directly contribute to solving this main equation. These might be separate problems, or pieces of a larger complex problem. But isolated as they are, they don't directly help in solving the provided equation.

So, to solve the main equation we need to proceed through several steps of algebraic simplification, including applying order of operations (PEMDAS/BODMAS), simplifying fractions and then isolating 'x'. Depending on the values obtained from the simplification, solving for 'x' might require either basic algebraic manipulation or some advanced methods like using the quadratic formula.

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Solve the equation for \( x \):\[\frac{(4 - 3.5 \cdot (2 \frac{1}{7} - 1 \frac{1}{5})) \div 0.16}{x} = \frac{3 \frac{2}{7} - \frac{3}{14} \div \frac{1}{6}}{41 \frac{23}{84} - 40 \frac{49}{60}}\]

Answer :

Final answer:

Explanation:

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Solve the equation for \( x \):

\[
\frac{(4 - 3.5 \cdot (2 \frac{1}{7} - 1 \frac{1}{5})) \div 0.16}{x} = \frac{3 \frac{2}{7} - \frac{3}{14} \div \frac{1}{6}}{41 \frac{23}{84} - 40 \frac{49}{60}}
\]