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

To solve the equation $-\frac{1}{8}x + 4 = 7x - \frac{4}{5}$, follow these steps:

Step 1: Move the $x$ terms to one side of the equation.
Add $\frac{1}{8}x$ to both sides:

$-\frac{1}{8}x + \frac{1}{8}x + 4 = 7x + \frac{1}{8}x - \frac{4}{5} \\ 4 = 7x + \frac{1}{8}x - \frac{4}{5}$

Step 2: Simplify by combining like terms. Combine $x$-terms on the right:

$4 = \left(7 + \frac{1}{8}\right)x - \frac{4}{5}$

Step 3: Express $7 + \frac{1}{8}$ as a single fraction: $\frac{56}{8} + \frac{1}{8} = \frac{57}{8}$.

Step 4: Substitute back:

$4 = \frac{57}{8}x - \frac{4}{5}$

Step 5: Move the constant term to the other side. Add $\frac{4}{5}$ to both sides:

$4 + \frac{4}{5} = \frac{57}{8}x \\ \frac{20}{5} + \frac{4}{5} = \frac{57}{8}x \\ \frac{24}{5} = \frac{57}{8}x$

Step 6: Solve for $x$ by dividing both sides by $\frac{57}{8}$ (multiply by $\frac{8}{57}$):

$x= \frac{24}{5} \times \frac{8}{57} \\ x = \frac{192}{285}$

Therefore, the solution to the problem is $x = \frac{192}{285}$.