Solve the equation. \[ |4 x-5|=8 \]

Step 1 ：The absolute value of a number is its distance from zero on the number line. Therefore, the equation \(|4x - 5| = 8\) means that \(4x - 5\) is either 8 units away from zero to the right (positive direction) or 8 units away from zero to the left (negative direction). This gives us two equations to solve: \(4x - 5 = 8\) and \(4x - 5 = -8\).

Step 2 ：Solving the first equation \(4x - 5 = 8\), we get the solution \(x = \frac{13}{4}\).

Step 3 ：Solving the second equation \(4x - 5 = -8\), we get the solution \(x = -\frac{3}{4}\).

Step 4 ：The solutions to the equation are \(\boxed{\frac{13}{4}}\) and \(\boxed{-\frac{3}{4}}\).