$\text{|-2x|=x-3}$
$\text{Ta có:}$
$\text{|-2x|=-2x khi -2x > 0 ⇔x<0}$
$\text{|-2x|=2x khi -2x<0 ⇔x>0}$
$\text{TH1 x<0}$
$\text{-2x=x-3}$
$\text{⇔-2x-x=-3}$
$\text{⇔-3x=-3}$
$\text{⇔x=1 (không thoả mãn)}$
$\text{TH2:x>0}$
$\text{2x=x-3}$
$\text{⇔2x-x=-3}$
$\text{⇔x=-3}$
$\text{⇔x=-3 (không thoả mãn)}$
$\text{Vậy phương trình vô nghiệm}$
$\text{b)|3x−1|−x=2}$
$\text{+)Với x ≥ $\frac{1}{3}$}$
$\text{⇒|3x−1|=3x−1}$
$\text{⇔ 3x−1−x=2}$
$\text{⇔ 2x=3}$
$\text{⇔ x=32(TM)}$
$\text{+)Với x < $\frac{1}{3}$}$
$\text{⇒|3x−1|=−3x+1}$
$\text{⇔ −3x+1−x=2}$
$\text{⇔ −4x=1}$
$\text{⇔ x=−14(TM)}$
$\text{c)|5x-4|=|x+1|}$
$\text{⇔(5x+4)²=(x+1)²}$
$\text{⇔25x²+40x+16=x²+2x+1}$
$\text{⇔25x²-x²+40x-2x+16-1=0}$
$\text{⇔24x²+38x+15=0}$
$\text{⇔24x²+18x+20x+15=0}$
$\text{⇔6x(4x+3)+5(4x+3)=0}$
$\text{⇔(4x+3)(6x+5)=0}$
⇔ \(\left[ \begin{array}{l}4x+3=0\\6x+5=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}4x=-3\\6x=-5\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\frac{-3}{4}\\x=\frac{-5}{6}\end{array} \right.\)
