Đáp án:
$a)|2x-5|=6$
$⇒\left[ \begin{array}{l}2x-5=6\\2x-5=-6\end{array} \right.$
$⇒\left[ \begin{array}{l}2x=11\\2x=-1\end{array} \right.$
$⇒\left[ \begin{array}{l}x=\dfrac{11}{2}\\x=\dfrac{-1}{2}\end{array} \right.$
$b)3|x-1|+7=10$
$⇔3|x-1|=-3$
$⇔|x-1|=-1(vô lí)$
$⇒$Phương trình vô nghiệm
$c)|2x+3|=|5-x|$
$⇔(2x+3)^2=(5-x)^2$
$⇔4x^2+12x+9=25-10x+x^2$
$⇔3x^2+22x-16=0$
$⇔3x^2+24x-2x-16=0$
$⇔3x(x+8)-2(x+8)=0$
$⇔(3x-2)(x+8)=0$
$⇔\left[ \begin{array}{l}x=\dfrac{2}{3}\\x=-8\end{array} \right.$
$d)|2+3x|=3|x-1|$
$⇔(2+3x)^2=9(x-1)^2$
$⇔4+12x+9x^2=9(x^2-2x+1)$
$⇔4+12x+9x^2=9x^2-18x+9$
$⇔30x=5$
$⇔x=\dfrac{1}{6}$
$e)|3x-1|=4x+2$
$⇔\left[ \begin{array}{l}3x-1=4x+2\\3x-1=-(4x+2)\end{array} \right.$
$⇔\left[ \begin{array}{l}x=-3\\x=\dfrac{-1}{7}\end{array} \right.$
$15)(x\neq1;-3)$
$\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}=1-\dfrac{4}{(x+1)(x-3)}$
$⇔\dfrac{3x-1}{x-1}-\dfrac{2x+5}{x+3}+\dfrac{4}{(x+1)(x-3)}=1$
$⇔\dfrac{(3x-1)(x+3)}{(x-1)(x+3)}-\dfrac{(2x+5)(x-1)}{(x+3)(x-1)}+\dfrac{4}{(x+1)(x-3)}=1$
$⇔\dfrac{3x^2+9x-x-3-(2x^2-2x+5x-5)+4}{(x-1)(x+3)}=1$
$⇔x^2+5x+6=(x-1)(x+3)$
$⇔x^2+5x+6=x^2+3x-x-3$
$⇔3x=-9$
$⇔x=-3$
