\(\left|\left|x+5\right|-4\right|=3\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x+5\right|-4=-3\\\left|x+5\right|-4=3\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left|x+5\right|=1\\\left|x+5\right|=7\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x+5=-1\\x+5=1\end{matrix}\right.\\\left\{{}\begin{matrix}x+5=-7\\x+5=7\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=-6\\x=-4\end{matrix}\right.\\\left\{{}\begin{matrix}x=-12\\x=2\end{matrix}\right.\end{matrix}\right.\)
Vậy.............
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||x+5| - 4 | = 3
TH1: |x+5|-4=3
\(\Leftrightarrow\)|x+5|=7
+) x+5=7\(\Rightarrow\)x = 2
+) x+5=-7\(\Rightarrow\) x =-12
TH2:|x+5|-4=-3
\(\Leftrightarrow\)| |x+5|= 1
+) x+5=1
\(\Rightarrow\) x =-4
+) x+5 = -1
\(\Rightarrow\) x =-6
Vậy x\(\in\)\(\left\{2;-12;-4;-6\right\}\)
\(\left|\right|x+5\left|-4\right|=3\Rightarrow\left[{}\begin{matrix}\left|x+5\right|-4=3\\\left|x+5\right|-4=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\left|x+5\right|=7\\\left|x+5\right|=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x+5=7\\x+5=-7\\x+5=1\\x+5=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=-12\\x=-4\\x=-6\end{matrix}\right.\)
Vậy \(x\in\left\{-12;-6;-4;2\right\}\)
||x+5| - 4 | = 3
TH1: |x+5|-4=3
⇔⇔|x+5|=7
+) x+5=7⇒⇒x = 2
+) x+5=-7⇒⇒ x =-12
TH2:|x+5|-4=-3
⇔⇔| |x+5|= 1
+) x+5=1
⇒⇒ x =-4
+) x+5 = -1
⇒⇒ x =-6
Vậy x∈{2;−12;−4;−6}
