Question 119874
To begin with, please stop writing your questions in ALL CAPS.  It is impolite, annoying, and is the electronic equivalent of shouting.


The perimeter of a polygon is the sum of the lengths of the sides.  You have expressions for the lengths of the three sides of this polygon, so add them together:


{{{(8x+3)+(6x+4)+(6x-3)=84}}} and the sum is 84 because you are told the perimeter is 84.


Now simplify by collecting like terms:


{{{(8x+6x+6x)+(3+4-3)=84}}}


{{{20x+4=84}}}


Add -4 to both sides


{{{20x+4-4=84-4}}}
{{{20x=80}}}


Divide by 20


{{{20x/20=80/20}}}
{{{x=4}}}


Now that we know x, we can go about computing the lengths of the three sides:


Side 1:  {{{8x+3=8(4)+3=32+3=35}}}


Side 2:  {{{6x+4=6(4)+4=24+4=28}}}


Side 3:  {{{6x-3=6(4)-3=24-3=21}}}


And there are your three answers.


Final step.  Check your answer.  We need to determine if the sum of our answers is actually 84 as the problem stated:


{{{35+28+21=84}}}, Done.


Hope that helps,
John