Reduce[-Abs[x]+3≥8x]

If x<0,
x+3≥8x
3≥7x
x≤7/3 && x<0 => x<0

If x≥0,
-x+3≥8x
3≥9x
x≤1/3

So, I have x<0 || (x≥0&&x≤1/3) as solutions. This simplifies to x≤1/3.

Solve[f==6x+18, x]