Solve for x:
2+(8 (54 x-36))/(9) = 90 x-(3 (16 x-40))/(4)
Put each term in 2+(8 (54 x-36))/9 over the common denominator 9: 2+(8 (54 x-36))/9 = 18/9+(8 (54 x-36))/9:
18/9+(8 (54 x-36))/9 = 90 x-(3 (16 x-40))/4
18/9+(8 (54 x-36))/9 = (18+8 (54 x-36))/9:
(18+8 (54 x-36))/9 = 90 x-(3 (16 x-40))/4
8 (54 x-36) = 432 x-288:
(432 x-288+18)/9 = 90 x-(3 (16 x-40))/4
Grouping like terms, 432 x-288+18 = 432 x+(18-288):
(432 x+(18-288))/9 = 90 x-(3 (16 x-40))/4
18-288 = -270:
(432 x+-270)/9 = 90 x-(3 (16 x-40))/4
Put each term in 90 x-(3 (16 x-40))/4 over the common denominator 4: 90 x-(3 (16 x-40))/4 = (360 x)/4-(3 (16 x-40))/4:
(432 x-270)/9 = (360 x)/4-(3 (16 x-40))/4
(360 x)/4-(3 (16 x-40))/4 = (360 x-3 (16 x-40))/4:
(432 x-270)/9 = (360 x-3 (16 x-40))/4
-3 (16 x-40) = 120-48 x:
(432 x-270)/9 = (360 x+120-48 x)/4
Grouping like terms, 360 x-48 x+120 = (360 x-48 x)+120:
(432 x-270)/9 = ((360 x-48 x)+120)/4
360 x-48 x = 312 x:
(432 x-270)/9 = (312 x+120)/4
Multiply both sides by 36:
(36 (432 x-270))/9 = (36 (312 x+120))/4
36/9 = (9×4)/9 = 4:
4 (432 x-270) = (36 (312 x+120))/4
36/4 = (4×9)/4 = 9:
4 (432 x-270) = 9 (312 x+120)
Expand out terms of the left hand side:
1728 x-1080 = 9 (312 x+120)
Expand out terms of the right hand side:
1728 x-1080 = 2808 x+1080
Subtract 2808 x from both sides:
(1728 x-2808 x)-1080 = (2808 x-2808 x)+1080
1728 x-2808 x = -1080 x:
-1080 x-1080 = (2808 x-2808 x)+1080
2808 x-2808 x = 0:
-1080 x-1080 = 1080
Add 1080 to both sides:
(1080-1080)-1080 x = 1080+1080
1080-1080 = 0:
-1080 x = 1080+1080
1080+1080 = 2160:
-1080 x = 2160
Divide both sides of -1080 x = 2160 by -1080:
(-1080 x)/(-1080) = 2160/(-1080)
(-1080)/(-1080) = 1:
x = 2160/(-1080)
The gcd of 2160 and -1080 is 1080, so 2160/(-1080) = (1080×2)/(1080 (-1)) = 1080/1080×2/(-1) = 2/(-1):
x = 2/(-1)
Multiply numerator and denominator of 2/(-1) by -1:
Answer: |x = -2
