Answer
$x=-\dfrac{1}{31}$
Work Step by Step
Multiplying both sides by $10$, then the solution to the given equation, $
0.7(3x+6)=1.1-(x-3)
$, is
\begin{array}{l}
7(3x+6)=11-10(x-3)
\\\\
21x+42=11-10x+30
\\\\
21x+10x=11+30-42
\\\\
31x=-1
\\\\
x=-\dfrac{1}{31}
.\end{array}
CHECKING:
\begin{array}{l}
0.7\left(3\left( -\dfrac{1}{31} \right)+6\right)=1.1-\left(-\dfrac{1}{31}-3\right)
\\\\
\dfrac{7}{10}\left(-\dfrac{3}{31}+6\right)=\dfrac{11}{10}-\left(-\dfrac{94}{31}\right)
\\\\
\dfrac{7}{10}\left(\dfrac{183}{31}\right)=\dfrac{11}{10}+\dfrac{94}{31}
\\\\
\dfrac{1281}{310}=\dfrac{1281}{310}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
x=-\dfrac{1}{31}
$.
