Answer
x = -2
Work Step by Step
$\frac{x+1}{3}$-$\frac{x-1}{6}$=$\frac{1}{6}$
6($\frac{x+1}{3}$-$\frac{x-1}{6}$)=6$\frac{1}{6}$
6$\frac{x+1}{3}$-6$\frac{x-1}{6}$=6$\frac{1}{6}$
2(x+1)-(x-1)=1
2x+2-x+1=1
x+3=1
x=1-3
x=-2
The solution is -2
Check
Let x=-2
$\frac{-2+1}{3}$-$\frac{-2-1}{6}$=$\frac{1}{6}$
-$\frac{1}{3}$-$\frac{-3}{6}$=$\frac{1}{6}$
-$\frac{2}{6}$+$\frac{3}{6}$=$\frac{1}{6}$
$\frac{1}{3}$=$\frac{1}{6}$