Solve the following equation. \[ 6-\frac{x}{7}=2+\frac{x}{7} \]

To solve the equation \( 6 - \frac{x}{7} = 2 + \frac{x}{7} \), we start by isolating \( x \). First, let’s eliminate the fractions by multiplying both sides of the equation by \( 7 \) to make it easier to work with: \[ 7 \left(6 - \frac{x}{7}\right) = 7\left(2 + \frac{x}{7}\right) \] This simplifies to: \[ 42 - x = 14 + x \] Next, we want to isolate \( x \). Begin by adding \( x \) to both sides: \[ 42 = 14 + 2x \] Then, subtract \( 14 \) from both sides: \[ 28 = 2x \] Now, divide both sides by \( 2 \) to solve for \( x \): \[ x = 14 \] Thus, the solution to the equation is: \[ \boxed{14} \]