Áp dụng Bđt \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\), ta có:
\(\left|4-2x\right|+\left|5-x\right|\ge\left|4-2x+5-x\right|=\left|3x-9\right|\)
\(\Rightarrow\left|3x-9\right|=7\)
\(\Rightarrow3x-9=\pm7\)
Xét \(3x-9=7\)
\(\Rightarrow3x=16\)
\(\Rightarrow x=\frac{16}{3}\)
Xét \(3x-9=-7\)
\(\Rightarrow3x=2\)
\(\Rightarrow x=\frac{2}{3}\)
\(\left|4-2x\right|+\left|5-x\right|=7\)
\(\Rightarrow\left[\begin{array}{nghiempt}4-2x+5-x=7\\4-2x+x-5=7\\2x-4+5-x=7\\2x-4+x-5=7\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}9-3x=7\\-x-1=7\\x+1=7\\3x-9=7\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{2}{3}\\x=-8\\x=6\\x=\frac{16}{3}\end{array}\right.\)
