By definition of absolute value, if [tex]x-1\ge0[/tex], then [tex]|x-1|=x-1[/tex], so
[tex]|x-1|=5x+2\implies x-1=5x+2\implies4x=-3\implies x=-\dfrac34[/tex]
On the other hand, if [tex]x-1<0[/tex], then [tex]|x-1|=-(x-1)=1-x[/tex], and
[tex]|x-1|=5x+2\implies1-x=5x+2\implies6x=-1\implies x=-\dfrac16[/tex]
