To solve the equation:

5 11/14 - 8/15x = 5/21

First, convert 5 11/14 to an improper fraction:

5 11/14 = 79/14

Now the equation becomes:

79/14 - 8/15x = 5/21

Find a common denominator for all fractions (14, 15, 21):

14 15 21 = 4410

Rewrite the equation with the common denominator:

(79 315 - 8 294x) / 4410 = 210 / 4410

Cross multiply:

79 315 - 8 294x = 210 * 4410

24945 - 2352x = 926100

Now simplify the equation:

-2352x = 901155

Divide by -2352:

x = 901155 / -2352

x ≈ -383.5

To solve the equation:

3x = 2/9

Divide by 3:

x = 2/9 * 1/3

x = 2/27

To solve the equation:

18/49 : x = 6/35

Rewrite the equation as a fraction:

(18/49) / x = 6/35

Now, divide the fractions:

18/49 / x = 6/35
18/49 * 35 = 6x
630/49 = 6x
630/49 = 6x
90/7 = 6x
x = 90/42
x = 15/7

Therefore, the solutions are:

x ≈ -383.5, x = 2/27, x = 15/7