To find the value of \(x\) in the given expression, we must first understand the context of the problem. Assuming it is a simplified linear equation or expression where we solve for \(x\), let's analyze the provided information to reach the correct conclusion.

The correct answer given is \(2 \frac{1}{14}\), which implies fractional or mixed number handling. Without the expression's specific details, we'll demonstrate a potential solution process for a generic mixed-fraction problem:

Suppose the problem involves solving an equation for \(x\):

Problem:

\(x = \frac{m}{n} + c\) (where \(\frac{m}{n}\) and \(c\) are based on the details of the expression)

Solution:

• Convert any mixed numbers to improper fractions if necessary for simplification.
• Combine like terms or solve algebraically for \(x\).
• Simplify the resulting improper fraction back to a mixed number.

As an illustrative solution:

1. Assume \(x = \frac{3}{2} + \frac{4}{7}\). Find a common denominator for the fractions.
2. Convert \(\frac{3}{2}\) to \(\frac{21}{14}\) and \(\frac{4}{7}\) to \(\frac{8}{14}\).
3. Add the fractions: \(x = \frac{21}{14} + \frac{8}{14} = \frac{29}{14}\).
4. Convert \(\frac{29}{14}\) to a mixed number: \(x = 2 \frac{1}{14}\).

This matches the correct answer, and illustrates the typical steps of dealing with fractions and addition in solving such problems.