Question 782018
You are mishandling your factor of 10 simplification.


Step carefully,
{{{0.5(3x+0.07)=20.6}}}
{{{5(3x+0.07)=206}}}
{{{3x+0.07=206/5}}}
{{{3x=206/5-0.07}}}
{{{x=(206/5-0.07)/3}}}
{{{x=206/15-0.07/3}}}
{{{x=206/15-(0.07)(5)/15}}}
{{{x=(206-0.35)/3}}}
and then simplify appropriately.  Do you find a different rational result?