Solve for n:
(-133)/36=(-2 (4/3-(n)/(3)))/(3)
4/3-(n)/(3)=(4-n)/3:
(-133)/36=(-2)/3 (4-n)/3
3×3 = 9:
(-133)/36=(-2 (4-n))/9
(-133)/36=(-2 (4-n))/9 is equivalent to (-2 (4-n))/9=(-133)/36:
(-2 (4-n))/9=(-133)/36
Multiply both sides of (-2 (4-n))/9=(-133)/36 by -9/2:
(-9 (-2) (4-n))/(2×9)=(-9)/2×(-133)/36
(-9)/2×(-133)/36=(-9 (-133))/(2×36):
(-9 (-2) (4-n))/(2×9)=(-9 (-133))/(2×36)
(-9)/9=(9 (-1))/9=-1:
(-2-1 (4-n))/2=(-9 (-133))/(2×36)
(-2)/2=(2 (-1))/2=-1:
--1 (4-n)=(-9 (-133))/(2×36)
(-1)^2=1:
4-n=(-9 (-133))/(2×36)
The gcd of -9 and 36 is 9, so (-9 (-133))/(2×36)=((9 (-1)) (-133))/(2 (9×4))=9/9×(-(-133))/(2×4)=(-(-133))/(2×4):
4-n=(-133-1)/(2×4)
2×4 = 8:
4-n=(-(-133))/8
-(-133) = 133:
4-n=133/8
Subtract 4 from both sides:
(4-4)-n=133/8-4
4-4=0:
-n=133/8-4
Put 133/8-4 over the common denominator 8. 133/8-4 = 133/8+(8 (-4))/8:
-n=133/8-(4×8)/8
8 (-4) = -32:
-n=133/8+-32/8
133/8-32/8 = (133-32)/8:
-n=(133-32)/8
133-32=101:
-n=101/8
Multiply both sides of -n=101/8 by -1:
(-n)/(-1)=(-101)/8
(-1)/(-1)=1:
Answer: | n=(-101)/8
