x=0\\\left \{ {{x-1<0} \atop {x-2<0}} \right.=>x<1\\2)x-1-x+2=x+3=>x=-2\\ \left \{ {{x-1}\geq0 \atop {x-2<0}} \right. =>1\leq x<2\\3)x-1+x-2=x+3=>x=6\\\left \{ {{x-1}\geq0 \atop {x-2}\geq0 } \right. =>x\geq 2" alt="|x-1|+|x-2|=x+3\\1)-x+1-x+2=x+3=>x=0\\\left \{ {{x-1<0} \atop {x-2<0}} \right.=>x<1\\2)x-1-x+2=x+3=>x=-2\\ \left \{ {{x-1}\geq0 \atop {x-2<0}} \right. =>1\leq x<2\\3)x-1+x-2=x+3=>x=6\\\left \{ {{x-1}\geq0 \atop {x-2}\geq0 } \right. =>x\geq 2" align="absmiddle" class="latex-formula">
Ответ:x={0;6}