Multiply through by 7: 7w-6w-1=2(w-2/5)=2w-4/5.
Collecting the w's together on the right and numbers on the left: -1+4/5=2w+6w-7w; -1/5=w or w=-1/5.
Check: substitute w=-1/5 in the original equation: -1/5+6/35-1/7=2/7(-1/5-2/5); (-7+6-5)/35=2/7(-3/5); -6/35=-6/35, so equation checks out.