Box toán 10 hình như phóng đại quá bạn ơi :v
Câu 2 bạn tự giải và biểu diễn nghiệm nhé, mình k biết vẽ biểu diễn :V
Bài 3 :
a) \(\left|2x+1\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=5\left(2x+1\ge0\right)\\-\left(2x+1\right)=5\left(2x+1< 0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=4\left(x\ge-\dfrac{1}{2}\right)\\-2x-1=5\left(x< -\dfrac{1}{2}\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(x\ge-\dfrac{1}{2}\right)\left(TMĐK\right)\\x=-3\left(x< -\dfrac{1}{2}\right)\left(TMĐK\right)\end{matrix}\right.\)
Vậy \(S=\left\{-3;2\right\}\)
b) \(\left|x\right|=2x+1\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2x+1\left(x\ge0\right)\\-x=2x+1\left(x< 0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\left(x\ge0\right)\left(KTMĐK\right)\\x=-\dfrac{1}{3}\left(x< 0\right)\left(TMĐK\right)\end{matrix}\right.\)
Vậy \(S=\left\{-\dfrac{1}{3}\right\}\)
c) \(\left|2x-5\right|=x-1\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-5=x-1\left(2x-5\ge0\right)\\-\left(2x-5\right)=x-1\left(2x-5< 0\right)\end{matrix}\right.\)
Giải giống trên : \(\Leftrightarrow\left[{}\begin{matrix}x=4\left(x\ge\dfrac{5}{2}\right)\left(TMĐK\right)\\x=2\left(x< \dfrac{5}{2}\right)\left(TMĐK\right)\end{matrix}\right.\)
Vậy \(S=\left\{2;4\right\}\)
d) \(\left|x+4\right|=2x-5\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=2x-5\left(x\ge-4\right)\\-\left(x+4\right)=2x-5\left(x< -4\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=9\left(TMĐK\right)\\x=\dfrac{1}{3}\left(KTMĐK\right)\end{matrix}\right.\)
Vậy \(S=\left\{9\right\}\)
