\(|x-4|-13\)
\(\Leftrightarrow \left[\begin{array}{} x-4=13\\ x-4=-13 \end{array} \right.\)
\(\Leftrightarrow \left[\begin{array}{} x=13+4\\ x=(-13)+4 \end{array} \right.\)
\(\Leftrightarrow \left[\begin{array}{} x=17\\ x=-9 \end{array} \right.\)
Vậy x ∈ {17;-9}
\(|x-4|-13=7\)
\(\Leftrightarrow |x-4|=7+13\)
\( \Leftrightarrow |x-4|=20\)
\(\Leftrightarrow \left[\begin{array}{} x-4=20\\ (x-4=-20 \end{array} \right.\)
\(\Leftrightarrow \left[\begin{array}{} x=20+4\\ x=(-20)+4 \end{array} \right.\)
\(\Leftrightarrow \left[\begin{array}{} x=24\\ x=-16 \end{array} \right.\)
Vậy x ∈{24;-16}
\(\left|\left|x-4\right|-13\right|=7\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-4\right|-13=7\\\left|x-4\right|-13=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left|x-4\right|=21\\\left|x-4\right|=6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x-4=21\\x-4=-21\end{matrix}\right.\\\left[{}\begin{matrix}x-4=6\\x-4=-6\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=25\\x=-17\end{matrix}\right.\\\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\end{matrix}\right.\)
Giải:
||x-4|-13|=7
⇒|x-4|-13=7
⇒|x-4| =7+13
⇒|x-4| =20
⇒ x-4=20 hoặc x-4=-20
x=24 hoặc x=-16
Vậy x ∈ {-16;24}
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