sinx-x<0.1 how do I find x?

$sin(x)<0.1$

${sin}^{-1}(sin(x))<{sin}^{-1}(0.1)$

$x<0.01001667421162...$

sinx-x<0.1 how do I find x?

$sin(x)-x<0.1\\ sin(x)<0.1+x\\ $

I would graph

y=sin(x)

and 

y=0.1+x

The statement will be true when the sin(x) curve is under the line.

https://www.desmos.com/calculator/rj5amyp3lh

You can see that this is true when  x > -0.854      (approximately)