Solve the Fraction Equation: Finding X in 1/8 - 4/16 + 15/16x = 3/4x - 2/8x + 3/8

To solve this problem, we'll follow these steps:

• Step 1: Simplify both sides of the equation by combining like terms.
• Step 2: Solve for $x$.

Now, let's work through each step:

Step 1: Simplify the left-hand side:
$\frac{1}{8} - \frac{4}{16} + \frac{15}{16}x = \frac{1}{8} - \frac{1}{4} + \frac{15}{16}x$.
Convert $\frac{1}{4}$ to $\frac{2}{8}$, the same denominator with $\frac{1}{8}$:
$\frac{1}{8} - \frac{2}{8} + \frac{15}{16}x = -\frac{1}{8} + \frac{15}{16}x$.

Simplify the right-hand side:
$\frac{3}{4}x - \frac{2}{8}x + \frac{3}{8} = \frac{3}{4}x - \frac{1}{4}x + \frac{3}{8}$.
Convert both terms with $x$ to a common denominator (i.e., 4/4 of $x$ terms):
$\frac{2}{4}x + \frac{3}{8} = \frac{1}{2}x + \frac{3}{8}$.

Step 2: Equate the simplified expressions:
$-\frac{1}{8} + \frac{15}{16}x = \frac{1}{2}x + \frac{3}{8}$.

Subtract $\frac{1}{2}x$ from both sides:
$-\frac{1}{8} + \frac{15}{16}x - \frac{1}{2}x = \frac{3}{8}$.
Convert $\frac{1}{2}x$ to $\frac{8}{16}x$ and $\frac{15}{16}x - \frac{8}{16}x = \frac{7}{16}x$.
$-\frac{1}{8} + \frac{7}{16}x = \frac{3}{8}$.

Add $\frac{1}{8}$ to both sides:
$\frac{7}{16}x = \frac{3}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2}$.

Solve for $x$ by multiplying both sides by the reciprocal of $\frac{7}{16}$:
$x = \frac{1/2 \times 16}{7} = \frac{16}{14} = \frac{8}{7}$.
Checking the choice that matches, the solution is $\frac{16}{14}$.

Therefore, the solution to the problem is $x = \frac{16}{14}$.