To solve the equation |х-5| = 0:

Since |х-5| represents the absolute value of the expression (х-5), the only way for it to equal 0 is if the expression (х-5) itself equals 0.

Thus, we have:

х - 5 = 0
х = 5

So the solution to |х-5| = 0 is x = 5.

To solve the equation |3х-1| = 0:

Following the same logic as above, since |3х-1| represents the absolute value of the expression (3х-1), the only way for it to equal 0 is if the expression (3х-1) itself equals 0.

Thus, we have:

3х - 1 = 0
3х = 1
х = 1/3

So the solution to |3х-1| = 0 is x = 1/3.