Giải thích các bước giải:
\(\begin{array}{l}
1)a)\left| {x - 1} \right| \ge 0;\left| {x - y + 5} \right| \ge 0\\
\Rightarrow \left| {x - 1} \right| + \left| {x - y + 5} \right| \ge 0\\
gt \Rightarrow \left\{ \begin{array}{l}
x - 1 = 0\\
x - y + 5 = 0
\end{array} \right.\\
\Rightarrow x = 1;y = 6\\
b)x\left( {y + 1} \right) + \left( {y + 1} \right) = 10\\
\left( {x + 1} \right)\left( {y + 1} \right) = 10\\
TH1:\left\{ \begin{array}{l}
x + 1 = 1\\
y + 1 = 10
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 0\\
y = 9
\end{array} \right.\\
TH2:\left\{ \begin{array}{l}
x + 1 = - 1\\
y + 1 = - 10
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = - 2\\
y = - 11
\end{array} \right.\\
TH3:\left\{ \begin{array}{l}
x + 1 = - 10\\
y + 1 = - 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = - 11\\
y = - 2
\end{array} \right.\\
TH4:\left\{ \begin{array}{l}
x + 1 = 10\\
y + 1 = 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 9\\
y = 0
\end{array} \right.\\
TH5:\left\{ \begin{array}{l}
x + 1 = 2\\
y + 1 = 5
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 1\\
y = 4
\end{array} \right.\\
TH6:\left\{ \begin{array}{l}
x + 1 = - 2\\
y + 1 = - 5
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = - 3\\
y = - 6
\end{array} \right.\\
TH7:\left\{ \begin{array}{l}
x + 1 = - 5\\
y + 1 = - 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = - 6\\
y = - 3
\end{array} \right.\\
TH8:\left\{ \begin{array}{l}
x + 1 = 5\\
y + 1 = 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 4\\
y = 1
\end{array} \right.\\
2)A = \left| {x - 3} \right| + 1 \ge 1\\
{A_{\min }} = 1 \Leftrightarrow x = 3\\
B = \left| {6 - 2x} \right| - 5 \ge - 5\\
{B_{\min }} = - 5 \Leftrightarrow x = 3\\
C = 3 - \left| {x + 1} \right| \le 3\\
{C_{\max }} = 3 \Leftrightarrow x = - 1\\
D = 11 - {\left( {x + 1} \right)^2} - \left| {2 - y} \right| \le 11\\
{D_{\max }} = 11 \Leftrightarrow \left\{ \begin{array}{l}
x = - 1\\
y = 2
\end{array} \right.
\end{array}\)
