Question 1094264
This equation does not require looking at intervals.


{{{abs(5x-4)=abs(x+17)}}}

The signs of the expressions inside the absolute value are either the same or they are opposite.


The signs being alike:
{{{5x-4=x+17}}}
{{{4x=17+4}}}
{{{highlight_green(x=21/4)}}}
Check this solution value:
{{{abs(5(21/4)-4)=abs(21/4+17)}}}
{{{(105-16)/4=21/4+68/4}}}
{{{(105-16)/4=89/4}}}
{{{89/4=89/4}}}------{{{solution}}} {{{works}}}



The signs being opposite:
{{{5x-4=-x-17}}}
{{{6x=-13}}}
{{{highlight_green(x=-13/6)}}}
Check this solution value:
{{{abs(5(-13/6)-4)=abs(-13/6+17)}}}
{{{(5*13)/6+4=17-13/6}}}
{{{65/6+24/6=(102-13)/6}}}
{{{89/6=89/6}}}------{{{solution}}} {{{works}}}


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The solution set:  {{{system(21/4,and,-13/6)}}}
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