Solve for x:
243 x - 9 = x/729 - 8
Put each term in x/729 - 8 over the common denominator 729: x/729 - 8 = x/729 - (5832)/729:
243 x - 9 = x/729 - (5832)/729
x/729 - (5832)/729 = (x - 5832)/729:
243 x - 9 = (x - 5832)/729
Multiply both sides by 729:
729 (243 x - 9) = (729 (x - 5832))/729
(729 (x - 5832))/729 = 729/729×(x - 5832) = x - 5832:
729 (243 x - 9) = x - 5832
Expand out terms of the left hand side:
177147 x - 6561 = x - 5832
Subtract x from both sides:
(177147 x - x) - 6561 = (x - x) - 5832
177147 x - x = 177146 x:
177146 x - 6561 = (x - x) - 5832
x - x = 0:
177146 x - 6561 = -5832
Add 6561 to both sides:
177146 x + (6561 - 6561) = 6561 - 5832
6561 - 6561 = 0:
177146 x = 6561 - 5832
6561 - 5832 = 729:
177146 x = 729
Divide both sides of 177146 x = 729 by 177146:
(177146 x)/177146 = 729/177146
177146/177146 = 1:
Answer: x = 729/177146
