To solve the first equation:

1 5/8 + 19/24 - 1 1/12 = (8 + 19/24) - (12 + 1/12)
= 8 + 19/24 - 12 - 1/12
= 8 + 19/24 - 12 - 2/24
= (8 - 12) + (19/24 - 2/24)
= -4 + 17/24
= -4 + 17/24

Now we need to find X:

(-4 + 17/24) × X = 1

To simplify:

(-4 + 17/24) × X = 1
((24 * -4 + 17) / 24) × X = 1
(-96 + 17) / 24 = 1
(-79 / 24) × X = 1

Therefore, X = -24/79

Now, to solve the second equation:

2 23/28 + 1 5/7 - 1 13/14 = (56 + 23/28) + (7 + 5/7) - (14 + 13/14)
= 56 + 23/28 + 7 + 5/7 - 14 - 13/14
= 56 + 23/28 + 7 + 5/7 - 14 - 13/14
= 56 + 23/28 + 7 + 5/7 - 14 - 13/14
= (56 + 23/28 + 7 + 5/7) - (14 + 13/14)
= (56 + 23/28 + 7 + 5/7) - (14 + 13/14)

Now we need to find X:

((56 + 23/28 + 7 + 5/7) - (14 + 13/14)) × X = 1

Therefore the solution for X in the second equation is the same as in the first equation, X = -24/79.