|1/2 - x/3|=5/6

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Of course not!

|1/2 - x/3| = 5/6
case1
1/2 - x/3 = 5/6
-x/3 = 5/6 - 1/2
-x/3 = 1/3
x = -1

case2:
-1/2 + x/3 = 5/6
x/3 = 4/3
x = 4

so x = -1 or x = 4

x = 7/2