Solve for X: Finding the Value in 2/14 - 3.5x + 1/7 = 3/21 + 5.5x

To solve this problem, let's go through the equation step by step:

Step 1: Simplify the fractional coefficients where possible.
We know $\frac{2}{14}$ simplifies to $\frac{1}{7}$ and $\frac{3}{21}$ simplifies to $\frac{1}{7}$. Substituting these into the equation results in:

$\frac{1}{7} - 3.5x + \frac{1}{7} = \frac{1}{7} + 5.5x$

Step 2: Combine like terms.
Combine $\frac{1}{7}$ and $\frac{1}{7}$ on the left side:

$\frac{2}{7} - 3.5x = \frac{1}{7} + 5.5x$

Step 3: Isolate the variable $x$.
Subtract $5.5x$ from both sides to move terms with $x$ to one side of the equation:

$\frac{2}{7} - 3.5x - 5.5x = \frac{1}{7}$

Simplify to:

$\frac{2}{7} - 9x = \frac{1}{7}$

Step 4: Move the constant terms to one side of the equation.
Subtract $\frac{2}{7}$ from both sides:

$-9x = \frac{1}{7} - \frac{2}{7}$

$-9x = -\frac{1}{7}$

Step 5: Solve for $x$ by dividing both sides by $-9$:

$x = \frac{-\frac{1}{7}}{-9} = \frac{1}{63}$

Therefore, the value of $x$ is $\frac{1}{63}$, which corresponds to choice number 1.