a) $\left| x-1 \right|+\left| x-4 \right|=3x$
Điều kiện: $x\ge 0$
Xét $0\le x < 1 \Rightarrow \left\{ \begin{align}& \left| x-1 \right|=1-x \\ & \left| x-4 \right|=4-x \\ \end{align} \right.$
$\Rightarrow \left| x-1 \right|+\left| x-4 \right|=1-x+4-x=5-2x=3x\Rightarrow x=1\textrm{ (loại do x < 1)}$
Xét $1\le x < 4 \Rightarrow \left\{ \begin{align}& \left| x-1 \right|=x-1 \\ & \left| x-4 \right|=4-x \\ \end{align} \right.$
$\Rightarrow \left| x-1 \right|+\left| x-4 \right|=x-1+4-x=3x\Rightarrow 3=3x\Rightarrow x=1 \textrm{(thỏa mãn)}$
Xét $4\le x \Rightarrow \left\{ \begin{align}& \left| x-1 \right|=x-1 \\ & \left| x-4 \right|=x-4 \\ \end{align} \right.$
$\Rightarrow \left| x-1 \right|+\left| x-4 \right|=x-1+x-4=2x-5=3x\Rightarrow x=-5\textrm{( loại)}$
Vậy $x = 1.$
b) $\left| x+1 \right|+\left| x+4 \right|=3x$
Điều kiện: $x\ge 0$
Khi $x\ge 0\Rightarrow \left\{ \begin{align}& \left| x+1 \right|=x+1 \\ & \left| x+4 \right|=x+4 \\ \end{align} \right.$
$\Rightarrow \left| x+1 \right|+\left| x+4 \right|=x+1+x+4=2x+5=3x\Rightarrow x=5$
Vậy $x = 5.$