Đáp án:
n) \(\left[ \begin{array}{l}
x = \dfrac{{53}}{3}\\
x = 99
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left| {x + 2} \right| + 23 = - 13\\
\to \left| {x + 2} \right| = - 10\left( {vô lý} \right)\\
Do:\left| {x + 2} \right| \ge 0\forall x \in R
\end{array}\)
⇒ Phương trình vô nghiệm
\(\begin{array}{l}
b)\left| x \right| + \left| {y + 1} \right| = 0\\
\to \left[ \begin{array}{l}
x = 0\\
y = - 1
\end{array} \right.\\
c){y^2} + 2 = 0\\
\to {y^2} = - 2\left( l \right)
\end{array}\)
\(\begin{array}{l}
d)\left| x \right| = 4\\
\to \left[ \begin{array}{l}
x = 4\\
x = - 4
\end{array} \right.\\
e)\left| {x - 1} \right| = 5\\
\to \left[ \begin{array}{l}
x - 1 = 5\\
x - 1 = - 5
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 6\\
x = - 4
\end{array} \right.\\
g)\left| {x + 5} \right| = - 17\left( l \right)\\
\to x \in \emptyset \\
f)\left| {7 - x} \right| = - 34\left( l \right)\\
\to x \in \emptyset \\
i)\left| {x - 4} \right| = 4\\
\to \left[ \begin{array}{l}
x - 4 = 4\\
x - 4 = - 4
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 8\\
x = 0
\end{array} \right.\\
l)9 \le \left| {x - 1} \right| < 11\\
\to \left[ \begin{array}{l}
9 \le x - 1 < 11\\
- 9 \ge x - 1 > - 11
\end{array} \right.\\
\to \left[ \begin{array}{l}
10 \le x < 12\\
- 8 \ge x > - 10
\end{array} \right.\\
n)x - \left( {57 + 42 + \left| {x + 23} \right|} \right) = 13 - \left( {47 + 25 - 32 + x} \right)\\
\to x - 99 + \left| {x + 23} \right| = - 27 - x\\
\to \left| {x + 23} \right| = 76 - 2x\\
\to \left[ \begin{array}{l}
x + 23 = 76 - 2x\\
x + 23 = - 76 + 2x
\end{array} \right.\\
\to \left[ \begin{array}{l}
3x = 53\\
x = 99
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{{53}}{3}\\
x = 99
\end{array} \right.
\end{array}\)
