You can subtract 1 from all of the "sides", just like you would in a regular inequality:
4color(white)(color(white)-1)<=x+1color(white)(color(white)-1)<8color(white)(color(white)-1)
4color(blue)-color(blue)1<=x+1color(blue)-color(blue)1<8color(blue)-color(blue)1
4color(blue)-color(blue)1<=xcolor(red)cancelcolor(black)(color(black)+1color(blue)-color(blue)1)<8color(blue)-color(blue)1
4color(blue)-color(blue)1<=xcolor(white)(color(white)+1-1)<8color(blue)-color(blue)1
3color(white)(color(white)-1)<=xcolor(white)(color(white)+1-1)<8color(blue)-color(blue)1
3color(white)(color(white)-1)<=xcolor(white)(color(white)+1-1)<7
That's the solution set. Hope this helped!