1) Simplifying the equation:

1/2x + 1/3x + 1/x = 26/27

Combining the fractions:

(3/6)x + (2/6)x + (6/6)x = 26/27

(11/6)x = 26/27

Multiplying both sides by 6 to get rid of the fraction:

11x = 156/27

11x = 5.77777778

x = 5.77777778/11

x = 0.525

2) Simplifying the equation:

1 5/12 - 5 3/5x = 2 2/3

Converting mixed numbers to improper fractions:

(112 + 5)/12 - (55 + 3)/5x = (2*3 + 2)/3

(17/12) - (28/5)x = 8/3

Multiplying each term by the least common denominator, which is 60:

17 5 - 28 12x = 8 * 20

85 - 336x = 160

336x = 85 - 160

336x = -75

x = -75/336

x = -0.22321429