Решить уравнение 4x+6-3(x+1)=5-2(x-3).

\[4x + 6 - 3(x + 1) = 5 - 2(x - 3)\]

\[4x + 6 - 3x - 3 = 5 - 2x + 6\]

\[x + 2x = 11 - 3\]

\[3x = 8\]

\[x = \frac{8}{3} = 2\frac{2}{3}\]

\[Ответ:x = 2\frac{2}{3}.\]