Question 1084538
{{{y=f(x)=abs(6-2x)+abs(x-1)-2x}}}

graph: just do several points and draw a graph that looks like this


{{{ graph( 600, 600, -30, 30, -30, 30,abs(6-2x)+abs(x-1)-2x) }}}


the range of the function:

{ {{{y}}} element {{{R}}} : {{{y>=-4}}} }


when is {{{f(x)>0 }}}? 

first find zeros:

{{{0 = -2x + sqrt((-2(x-3)^2)) + sqrt((x -1)^2)}}}


{{{0=-2x + -2(x- 3) + (x - 1)}}}

{{{2x =  - 2x+6+ x - 1}}}

{{{2x = 5 - x}}}

{{{2x+x = 5}}}

{{{3x = 5}}}

{{{x = 5/3}}} 

{{{0=-2x -(-2(x - 3)) +(x - 1)}}}

{{{0=-2x +2(x - 3)) +x - 1}}}

{{{0=-2x +2x - 6 +x -1}}}

{{{0= - 7 +x }}}

{{{x = 7}}}


so, {{{f(x)>0 }}} from {{{-infinity}}} to {{{ 5/3}}}  and from {{{7}}} to {{{ infinity}}}