a, \(|-2x|=3x+4\)
ĐK: 3x+4 \(\ge0\)
<=> 3x\(\ge-4\)
<=> x\(\ge\dfrac{-4}{3}\)
Ta có: \(\left[{}\begin{matrix}-2x=3x+4\\2x=3x+4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-4}{5}\\x=-4\end{matrix}\right.\) mà x\(\ge\dfrac{-4}{3}\)
Vậy S=\(\left\{\dfrac{-4}{5}\right\}\)
b, \(|-2,5x|=5+1,5x\)
ĐK: 5+1,5x\(\ge0\)
<=> 1,5x\(\ge-5\)
<=> x\(\ge\dfrac{-10}{3}\)
Ta có: \(\left[{}\begin{matrix}-2,5x=5+1,5x\\2,5x=5+1,5x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1,25\\x=5\end{matrix}\right.\)
(thỏa mãn ĐK x\(\ge\dfrac{-10}{3}\))
Vậy S= \(\left\{-1,25;5\right\}\)
a,\(\left|-2x\right|=3x+4\)
\(Khi:-2x\ge0\Rightarrow x\le0\)
\(\Rightarrow-2x=3x+4\)
\(\Leftrightarrow-2x-3x=4\) \(\Leftrightarrow-5x=4\)
\(\Leftrightarrow x=\dfrac{-4}{5}\)(t/m)
Khi \(-2x< 0\Rightarrow x>0\)
\(\Rightarrow2x=3x+4\) \(\Leftrightarrow\) \(2x-3x=4\)
\(\Leftrightarrow-x=4\) \(\Leftrightarrow\) \(x=-4\)(k t/m)
Vậy tập nghiệm của pt là: \(S=\left\{-\dfrac{4}{5}\right\}\)
b. \(\left|-2,5x\right|=5+1,5x\)
Khi \(-2,5x\ge0\Rightarrow x\le0\)
\(\Rightarrow-2,5x=5+1,5x\)
\(\Leftrightarrow-2,5x-1,5x=5\) \(\Leftrightarrow\) \(-4x=5\Leftrightarrow x=-\dfrac{5}{4}\) (t/m)
Khi \(-2,5x< 0\Rightarrow x>0\)
\(\Rightarrow2,5x=5+1,5x\) \(\Leftrightarrow\) \(2,5x-1,5x=5\)
\(\Leftrightarrow x=5\)(t/m)
Vậy tập nghiệm của pt: \(S=\left\{-\dfrac{5}{4};5\right\}\)
