\(\left|2x+3\right|-2.\left|4-x\right|=5\)
+ TH1: \(x< -\frac{3}{2}.\)
\(\Leftrightarrow-\left(2x+3\right)-2.\left(4-x\right)=5\)
\(\Rightarrow-2x-3-\left(8-2x\right)=5\)
\(\Rightarrow-2x-3-8+2x=5\)
\(\Rightarrow-11=5\left(vôlí,loại\right).\)
+ TH2: \(-\frac{3}{2}< x< 4.\)
\(\Leftrightarrow\left(2x+3\right)-2.\left(4-x\right)=5\)
\(\Rightarrow2x+3-\left(8-2x\right)=5\)
\(\Rightarrow2x+3-8+2x=5\)
\(\Rightarrow4x-5=5\)
\(\Rightarrow4x=5+5\)
\(\Rightarrow4x=10\)
\(\Rightarrow x=10:4\)
\(\Rightarrow x=\frac{5}{2}\left(TM\right).\)
+ TH3: \(x>4.\)
\(\Leftrightarrow\left(2x+3\right)-2.\left(x-4\right)=5\)
\(\Rightarrow2x+3-\left(2x-8\right)=5\)
\(\Rightarrow2x+3-2x+8=5\)
\(\Rightarrow11=5\left(vôlí,loại\right).\)
Vậy \(x=\frac{5}{2}.\)
Chúc bạn học tốt!
