1) |x-1| = 1.8

We need to determine the value of x that satisfies this equation. Since absolute value represents the distance of a number from zero on the number line, we can rewrite the equation as:

x - 1 = 1.8 or x - 1 = -1.8

Solving for x in the first case:
x = 1.8 + 1
x = 2.8

Solving for x in the second case:
x = -1.8 + 1
x = -0.8

Therefore, the solutions to the equation |x-1| = 1.8 are x = 2.8 and x = -0.8.

2) 3|x| + 1 = |x|

We need to determine the value of x that satisfies this equation. Again, we can rewrite the equation using the definition of absolute value:

3x + 1 = x or 3x + 1 = -x

Solving for x in the first case:
3x - x = -1
2x = -1
x = -1/2

Solving for x in the second case:
3x + x = -1
4x = -1
x = -1/4

Therefore, the solutions to the equation 3|x| + 1 = |x| are x = -1/2 and x = -1/4.

3) |2-|x|| = 0

Here the absolute value of a value is always positive, hence it cannot equal to 0 unless the value inside the absolute value is 0.

Therefore, in this case, |x| must equal 2 in order for the equation to hold true. Hence, the solution is x = 2.