To solve the equation x.8 = 4.x + 1, we can start by simplifying both sides of the equation.

On the left side, x.8 can be rewritten as 0.8x.

On the right side, 4.x can be rewritten as 4x.

So the equation becomes 0.8x = 4x + 1.

Next, we can move all the terms with x to one side of the equation and the constant term to the other side.

Subtracting 4x from both sides, we get -3.2x = 1.

Finally, we can solve for x by dividing both sides of the equation by -3.2.

Dividing both sides by -3.2, we get x = -1/3.2 or approximately x = -0.3125.