\(15.\left|x+8\right|-x=23\)
\(\Leftrightarrow15.\left|x+8\right|=23+x\)
\(\Leftrightarrow\left|x+8\right|=\left(23+x\right):15\)
\(\Leftrightarrow\left|x+8\right|=\dfrac{23}{15}+\dfrac{x}{15}\)
Xét trường hợp 1: \(x+8=\dfrac{23}{15}+\dfrac{x}{15}\)
\(\Rightarrow x+8-\dfrac{23}{15}-\dfrac{x}{15}=0\)
\(\Rightarrow x-\dfrac{x}{15}+\dfrac{97}{15}=0\)
\(\Rightarrow\dfrac{15x}{15}-\dfrac{x}{15}+\dfrac{97}{15}=0\)
\(\Rightarrow\dfrac{15x-x+97}{15}=0\)
\(\Rightarrow\dfrac{14x+97}{15}=0\)
\(\Rightarrow14x+97=0.15\)
\(\Rightarrow14x+97=0\)
\(\Rightarrow14x=-97\)
\(\Rightarrow x=-97:14\)
\(\Rightarrow x=\dfrac{-97}{14}\)
Xét trường hợp 2: \(x+8=-\left(\dfrac{23}{15}+\dfrac{x}{15}\right)\)
\(\Rightarrow x+8+\dfrac{23}{15}+\dfrac{x}{15}=0\)
\(\Rightarrow x+\dfrac{x}{15}+\dfrac{143}{15}=0\)
\(\Rightarrow\dfrac{15x}{15}+\dfrac{x}{15}+\dfrac{143}{15}=0\)
\(\Rightarrow\dfrac{15x+x+143}{15}=0\)
\(\Rightarrow\dfrac{16x+143}{15}=0\)
\(\Rightarrow16x+143=0.15\)
\(\Rightarrow16x+143=0\)
\(\Rightarrow16x=-143\)
\(\Rightarrow x=-143:16\)
\(\Rightarrow x=\dfrac{-143}{16}\)
Vậy \(x=\dfrac{-97}{14}\) hoặc \(x=\dfrac{-143}{16}\)
