\[\boxed{\text{118\ (}\text{с}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \ 2 \cdot (x + 3) = 2x + 6\]
\[2x + 6 = 2x + 6 \Longrightarrow верно\ при\ \]
\[любом\ x.\]
\[2)\ \ 2y = 4y\]
\[4y - 2y = 0\]
\[2y = 0\]
\[y = 0 \Longrightarrow корень\ уравнения.\]
\[3)\ 4 \cdot (c - 2) = 3c - 6\]
\[4c - 8 - 3c + 6 = 0\]
\[c = 2 \Longrightarrow корень\ уравнения.\]
\[4)\ 3x + 11 = 3 \cdot (x + 4)\]
\[3x + 11 - 3x - 12 = 0\]
\[- 1 = 0 \Longrightarrow неверно\ \]
\[при\ любом\ x.\]
\[Ответ:4)\ 3x + 11 = 3 \cdot (x + 4).\]
\[\boxed{\text{118\ (}\text{н}\text{).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ 3x + 11 = 3 \cdot (x + 4) - 1\]
\[3x + 11 = 3x + 12 - 1\]
\[3x + 11 = 3x + 11\]
\[Уравнение\ имеет\ бесконечного\ \]
\[много\ корней.\]
\[Например,\ x = 2:\]
\[3 \cdot 2 + 11 = 3 \cdot 2 + 11\]
\[6 + 11 = 6 + 11\]
\[17 = 17.\]
\[\textbf{б)}\ 33x = 18x\]
\[33x - 18x = 0\]
\[15x = 0\]
\[x = 0\ :15\]
\[x = 0.\]
\[Уравнение\ имеет\ один\ корень:\]
\[x = 0.\]