\(\left|2x+3\right|-2.\left|4-x\right|=5\)
Ta có 3 trường hợp
TH1: \(x\le-\frac{3}{2}\)
\(\Rightarrow-\left(2x+3\right)-2.\left(4-x\right)=5\)
\(\Rightarrow-2x-3-2.\left(4-x\right)=5\)
\(\Rightarrow-2x-3-8+2x=5\)
\(\Rightarrow0x-11=5\)
\(\Rightarrow0x=5+11\)
\(\Rightarrow0x=16\)
\(\Rightarrow x\in\varnothing\left(loại\right).\)
TH2: \(-\frac{3}{2}< x\le4\)
\(\Rightarrow\left(2x+3\right)-2.\left(4-x\right)=5\)
\(\Rightarrow2x+3-8+2x=5\)
\(\Rightarrow4x-5=5\)
\(\Rightarrow4x=10\)
\(\Rightarrow x=10:4\)
\(\Rightarrow x=\frac{5}{2}\left(TM\right)\)
TH3: \(x>4\)
\(\Rightarrow\left(2x+3\right)-2.\left(x-4\right)=5\)
\(\Rightarrow2x+3-2x+8=5\)
\(\Rightarrow0x+11=5\)
\(\Rightarrow0x=5-11\)
\(\Rightarrow0x=-6\)
\(\Rightarrow x\in\varnothing\left(loại\right).\)
Vậy \(x\in\left\{\frac{5}{2}\right\}.\)
Chúc bạn học tốt!
