Solve for x:
(8-x)/4+(x+2)/2 = x+9
Put each term in (8-x)/4+(x+2)/2 over the common denominator 4: (8-x)/4+(x+2)/2 = (8-x)/4+(2 (x+2))/4:
(8-x)/4+(2 (x+2))/4 = x+9
(8-x)/4+(2 (x+2))/4 = ((8-x)+2 (x+2))/4:
(8-x+2 (x+2))/4 = x+9
2 (x+2) = 2 x+4:
(2 x+4-x+8)/4 = x+9
Grouping like terms, 2 x-x+4+8 = (-x+2 x)+(8+4):
((-x+2 x)+(8+4))/4 = x+9
2 x-x = x:
(x+(8+4))/4 = x+9
8+4 = 12:
(x+12)/4 = x+9
Multiply both sides by 4:
(4 (x+12))/4 = 4 (x+9)
(4 (x+12))/4 = 4/4×(x+12) = x+12:
x+12 = 4 (x+9)
Expand out terms of the right hand side:
x+12 = 4 x+36
Subtract 4 x from both sides:
(x-4 x)+12 = (4 x-4 x)+36
x-4 x = -3 x:
-3 x+12 = (4 x-4 x)+36
4 x-4 x = 0:
12-3 x = 36
Subtract 12 from both sides:
(12-12)-3 x = 36-12
12-12 = 0:
-3 x = 36-12
36-12 = 24:
-3 x = 24
Divide both sides of -3 x = 24 by -3:
(-3 x)/(-3) = 24/(-3)
(-3)/(-3) = 1:
x = 24/(-3)
The gcd of 24 and -3 is 3, so 24/(-3) = (3×8)/(3 (-1)) = 3/3×8/(-1) = 8/(-1):
x = 8/(-1)
Multiply numerator and denominator of 8/(-1) by -1:
Answer: |x = -8
