Answer:
x = (-38)/3
Explanation:
Solve for x:
x/2 - (3 (x - 20/9))/4 = 29/6
Put each term in x - 20/9 over the common denominator 9: x - 20/9 = (9 x)/9 - 20/9:
x/2 - (3 (9 x)/9 - 20/9)/4 = 29/6
(9 x)/9 - 20/9 = (9 x - 20)/9:
x/2 - (3 (9 x - 20)/9)/4 = 29/6
4×9 = 36:
x/2 - (3 (9 x - 20))/36 = 29/6
The gcd of -3 and 36 is 3, so (-3 (9 x - 20))/36 = ((3 (-1)) (9 x - 20))/(3×12) = 3/3×(-(9 x - 20))/12 = (-(9 x - 20))/12:
x/2 + (-1 (9 x - 20))/12 = 29/6
Put each term in x/2 - (9 x - 20)/12 over the common denominator 12: x/2 - (9 x - 20)/12 = (6 x)/12 + (20 - 9 x)/12:
(6 x)/12 + (20 - 9 x)/12 = 29/6
(6 x)/12 + (20 - 9 x)/12 = (6 x + (20 - 9 x))/12:
(6 x - 9 x + 20)/12 = 29/6
Grouping like terms, 6 x - 9 x + 20 = 20 + (6 x - 9 x):
(20 + (6 x - 9 x))/12 = 29/6
6 x - 9 x = -3 x:
(-3 x + 20)/12 = 29/6
Multiply both sides of (20 - 3 x)/12 = 29/6 by 12:
(12 (20 - 3 x))/12 = 12×29/6
12×29/6 = (12×29)/6:
(12 (20 - 3 x))/12 = (12×29)/6
(12 (20 - 3 x))/12 = 12/12×(20 - 3 x) = 20 - 3 x:
20 - 3 x = (12×29)/6
12/6 = (6×2)/6 = 2:
20 - 3 x = 2×29
2×29 = 58:
20 - 3 x = 58
Subtract 20 from both sides:
(20 - 20) - 3 x = 58 - 20
20 - 20 = 0:
-3 x = 58 - 20
58 - 20 = 38:
-3 x = 38
Divide both sides of -3 x = 38 by -3:
(-3 x)/(-3) = 38/(-3)
(-3)/(-3) = 1:
x = 38/(-3)
Multiply numerator and denominator of 38/(-3) by -1:
Answer: x = (-38)/3