To solve the given algebraic equation:

(2/3 + 5/7x) * 21 = 294

First simplify the expression within the parentheses:

(2/3 + 5/7x) * 21

= (14/21 + 15/21x) * 21
= 14 + 15x

Now, substitute the simplified expression back into the equation:

14 + 15x = 294
15x = 280
x = 18 2/3

Now, substitute the value of x back into the second equation:

294 1/3(18 2/3) - 2 2/3(18 2/3) = 5
294 1/3(56/3) - 8 1/3(56/3) = 5
196 - 18 2/3 = 5
177 1/3 = 5

Since the equation is not balanced, there may be a mistake in the calculations. Let me know if you need further assistance.