Question 353525
{{{abs(x+1)=x+1}}} when {{{x+1>0}}}
{{{abs(x+1)=-(x+1)}}} when {{{x+1<0}}}
{{{x<-1}}}
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{{{abs(x+1)=x+1}}} when {{{x>-1}}}
{{{abs(x+1)=-x-1)}}} when {{{x<-1}}}
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{{{abs(x-1)=x-1}}} when {{{x-1>0}}}
{{{abs(x-1)=-(x-1)}}} when {{{x-1<0}}}
{{{x<1}}}
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{{{abs(x+1)=x-1}}} when {{{x>1}}}
{{{abs(x+1)=-x+1)}}} when {{{x<1}}}
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So now build the function and use the two critical points {{{x=-1}}} and {{{x=1}}}.
When {{{x<-1}}}
{{{f(x)=-x-1+(-x+1)=-2x}}}
When {{{-1<x<1}}}
{{{f(x)=x+1+(-x+1)=2}}}
When {{{x>1}}}
{{{f(x)=x+1+(x-1)=2x}}}
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Now graph it. 
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{{{drawing(300,300,-6,6,-2,10,grid(1),circle(-1,2,0.2),circle(1,2,0.2),graph(300,300,-6,6,-2,10,abs(x+1)+abs(x-1)))}}}