|5x-4|=5

To solve the equation \(|5x - 4| = 5\), we need to consider two cases because the absolute value can produce both positive and negative outcomes:

Case 1:
\(5x - 4 = 5\)
To solve for \(x\), add 4 to both sides:
\[ 5x = 9 \]
Now, divide by 5:
\[ x = \frac{9}{5} \]
or
\[ x = 1.8 \]

Case 2:
\(5x - 4 = -5\)
To solve for \(x\), add 4 to both sides:
\[ 5x = -1 \]
Now, divide by 5:
\[ x = -\frac{1}{5} \]
or
\[ x = -0.2 \]

Thus, the solutions to the equation \(|5x - 4| = 5\) are:
\[ x = \frac{9}{5} \quad \text{and} \quad x = -\frac{1}{5} \]