Solve for X: -7/8x + 1/7 - 1/3 = 2/3 + 5/8x - 1/4x Linear Equation

Let's proceed with solving the equation step-by-step:

Given Equation: $-\frac{7}{8}x + \frac{1}{7} - \frac{1}{3} = \frac{2}{3} + \frac{5}{8}x - \frac{1}{4}x$.

Step 1: Combine like terms on the right side of the equation.
On the right: $\frac{5}{8}x - \frac{1}{4}x = \frac{5}{8}x - \frac{2}{8}x = \frac{3}{8}x$.

Therefore, the equation becomes:
$-\frac{7}{8}x + \frac{1}{7} - \frac{1}{3} = \frac{2}{3} + \frac{3}{8}x$.

Step 2: Move all the terms involving $x$ to one side and constant terms to the other side:
$-\frac{7}{8}x - \frac{3}{8}x = \frac{2}{3} - \frac{1}{7} + \frac{1}{3}$.

Combine the terms involving $x$:
$-\frac{10}{8}x = \frac{2}{3} - \frac{1}{7} + \frac{1}{3}$.

Step 3: Simplify constants on the right side:
Combine constants on the right: $\frac{2}{3} + \frac{1}{3} = 1$
Thus, $1 - \frac{1}{7} = \frac{7}{7} - \frac{1}{7} = \frac{6}{7}$.

Now the equation is:
$-\frac{10}{8}x = \frac{6}{7}$.

Step 4: Simplify the coefficient of $x$:
$-\frac{10}{8} = -\frac{5}{4}$.
So the equation simplifies to:
$-\frac{5}{4}x = \frac{6}{7}$.

Step 5: Solve for $x$ by multiplying both sides by the reciprocal of $-\frac{5}{4}$:
$x = \frac{6}{7} \times \left(-\frac{4}{5}\right)$.

Step 6: Calculate the value of $x$:
$x = -\frac{24}{35}$.

Therefore, the solution to the equation is $x = -\frac{24}{35}$.

Given the provided choices, the correct answer is choice 4: $-\frac{24}{35}$.