Solve for X: Finding X in -1/4x + 8 = 3x - 1/2

To solve the equation $-\frac{1}{4}x + 8 = 3x - \frac{1}{2}$, follow these steps:

• Step 1: Remove fractions by multiplying every term by the least common multiple of the denominators, which is 4.
  This gives $4 \left(-\frac{1}{4}x\right) + 4 \times 8 = 4 \times 3x - 4 \times \frac{1}{2}$, simplifying to $-x + 32 = 12x - 2$.
• Step 2: Move all terms involving $x$ to one side by adding $x$ to both sides.
  This gives $32 = 13x - 2$.
• Step 3: Isolate $x$ by moving the constant to the other side: Add 2 to both sides to obtain $32 + 2 = 13x$, simplifying to $34 = 13x$.
• Step 4: Solve for $x$ by dividing both sides by 13, leading to $x = \frac{34}{13}$.
• Step 5: Simplify the fraction if possible. Here, $\frac{34}{13}$ is already in its simplest form. Converting to a mixed number, we get $2\frac{8}{13}$.

Therefore, the solution to the equation is $x = 2\frac{8}{13}$.