To solve the first equation, we need to clear the fractions by multiplying through by the least common multiple of the denominators, which is 6.
(5/6)x + 1 2/3 = 2x - 35x/6 + 5/3 = 2x - 35x/6 + 10/6 = 2x - 35x + 10 = 12x - 1810 = 7x - 1828 = 7xx = 4
Thus, the solution to the first equation is x = 4.
Next, let's solve the second equation:
(2/9)x - 1 1/3 = x + 12/9x - 4/3 = x + 12/9x - 4/3 = 3/3x + 3/32/9x - 4/3 = 3/3x + 3/32/9x - 4/3 = 3x/3 + 3/32/9x - 4/3 = 3x/3 + 3/32x - 12 = 9x + 92x - 9x = 12 + 9-7x = 21x = -3
Therefore, the solution to the second equation is x = -3.
To solve the first equation, we need to clear the fractions by multiplying through by the least common multiple of the denominators, which is 6.
(5/6)x + 1 2/3 = 2x - 3
5x/6 + 5/3 = 2x - 3
5x/6 + 10/6 = 2x - 3
5x + 10 = 12x - 18
10 = 7x - 18
28 = 7x
x = 4
Thus, the solution to the first equation is x = 4.
Next, let's solve the second equation:
(2/9)x - 1 1/3 = x + 1
2/9x - 4/3 = x + 1
2/9x - 4/3 = 3/3x + 3/3
2/9x - 4/3 = 3/3x + 3/3
2/9x - 4/3 = 3x/3 + 3/3
2/9x - 4/3 = 3x/3 + 3/3
2x - 12 = 9x + 9
2x - 9x = 12 + 9
-7x = 21
x = -3
Therefore, the solution to the second equation is x = -3.