đề bài là j vậy bn???
Ta có: \(\left|x+2,5\right|+\left|x+6,5\right|+\left|x+9,5\right|=7\)
\(\Rightarrow\left(\left|x+2,5\right|+\left|x+9,5\right|\right)+\left|x+6,5\right|=7\)
Ta có: \(\left|x+2,5\right|+\left|x+9,5\right|=\left|x+2,5\right|+\left|-x-9,5\right|\ge\left|x+2,5-x-9,5\right|=\left|-7\right|=7\) ( * )
Dấu " = " xảy ra
\(\Leftrightarrow\left(x+2,5\right).\left(-x-9,5\right)\ge0\)
\(\Leftrightarrow-9,5\le x\le-2,5\)
Ta có: \(\left|x+6,5\right|\ge0\) ( ** )
Dấu " = " xảy ra
\(\Leftrightarrow\left|x+6,5\right|=0\)
\(\Leftrightarrow x+6,5=0\)
\(\Leftrightarrow x=-6,5\)
Từ ( * ) ; ( ** )
\(\Rightarrow\left|x+2,5\right|+\left|x+6,5\right|+\left|x+9,5\right|\ge7+0\)
\(\Rightarrow\left|x+2,5\right|+\left|x+6,5\right|+\left|x+9,5\right|\ge7\)
\(\Rightarrow GTNN\) của \(\left|x+2,5\right|+\left|x+6,5\right|+\left|x+9,5\right|=7\)
Dấu " = " xảy ra
\(\Leftrightarrow\hept{\begin{cases}-9,5\le x\le-2,5\\x=-6,5\end{cases}}\)
\(\Leftrightarrow x=-6,5\)
\(\left|x+2,5\right|+\left|x+6,5\right|+\left|x+9,5\right|=7\)\
\(\left|x+x+x\right|+\left|2,5+6,5+9,5\right|=7\)
\(\left|x.3\right|+\left|18,5\right|=7\)
\(\left|x.3\right|=7-18,5\)
\(\left|x.3\right|=-11,5\)
\(x.3=-11,5\left(TH1\right)\)
\(x=-11,5:3\)
\(x=\frac{-23}{6}\)
\(x.3=11,5\left(TH2\right)\)
\(x=11,5:3\)
\(x=\frac{23}{6}\)
\(\Rightarrow x=\frac{-23}{6}hayx=\frac{23}{6}\)
