a) \(A=\left|3x-1\right|-\left(x-7\right)\)
th1: \(3x-1\ge0\Leftrightarrow3x\ge1\Leftrightarrow x\ge\dfrac{1}{3}\)
\(\Rightarrow A=\left|3x-1\right|-\left(x-7\right)=3x-1-x+7=2x+6>0\) \(\left(vì:x\ge\dfrac{1}{3}\right)\)
th2 : \(3x-1< 0\Leftrightarrow3x< 1\Leftrightarrow x< \dfrac{1}{3}\)
\(\Rightarrow A=\left|3x-1\right|-\left(x-7\right)=1-3x-x+7=8-4x>0\) \(\left(vì:x< \dfrac{1}{3}\right)\)
vậy \(A=2x+6;A=8-4x\)
b) \(\left|A\right|=8\)
th1: \(A=2x+6\)
\(\Rightarrow\left|2x+6\right|=8\Leftrightarrow2x+6=8\Leftrightarrow2x=2\Leftrightarrow x=1\) vậy \(x=1\) (tmđk)
th2: \(A=8-4x\)
\(\Rightarrow\left|8-4x\right|=8\Leftrightarrow8-4x=8\Leftrightarrow4x=0\Leftrightarrow x=0\) (tmđk)
