Solve for x:
(x-1)/2+(x+5)/2 = (x-1)/3
(x-1)/2+(x+5)/2 = ((x+5)+(x-1))/2:
(x+x-1+5)/2 = (x-1)/3
Grouping like terms, x+x-1+5 = (x+x)+(-1+5):
((x+x)+(-1+5))/2 = (x-1)/3
x+x = 2 x:
(2 x+(-1+5))/2 = (x-1)/3
5-1 = 4:
(2 x+4)/2 = (x-1)/3
Multiply both sides by 6:
(6 (2 x+4))/2 = 2 (x-1)
6/2 = (2×3)/2 = 3:
3 (2 x+4) = (6 (x-1))/3
6/3 = (3×2)/3 = 2:
3 (2 x+4) = 2 (x-1)
Expand out terms of the left hand side:
6 x+12 = 2 (x-1)
Expand out terms of the right hand side:
6 x+12 = 2 x-2
Subtract 2 x from both sides:
(6 x-2 x)+12 = (2 x-2 x)-2
6 x-2 x = 4 x:
4 x+12 = (2 x-2 x)-2
2 x-2 x = 0:
4 x+12 = -2
Subtract 12 from both sides:
4 x+(12-12) = -2-12
12-12 = 0:
4 x = -2-12
-2-12 = -14:
4 x = -14
Divide both sides of 4 x = -14 by 4:
(4 x)/4 = (-14)/4
4/4 = 1:
x = (-14)/4
The gcd of -14 and 4 is 2, so (-14)/4 = (2 (-7))/(2×2) = 2/2×(-7)/2 = (-7)/2:
Answer: |x = (-7)/2
