Question 917636
Description of the sides of your triangle:
18; and -3+2x; and x.


According to the THEOREM you quoted, picking any two sides should conform to the theorem as stated.


{{{2x-3+x>18}}}, picking the side #2 and side #3 to compare to side #1.
{{{3x-3>18}}}
{{{3x>21}}}
{{{x>7}}}
{{{highlight(x>7)}}}


Now you also need to examine comparing sum of sides 1 and 3 with length of side 2, using the triangle inequality theorem.  THEN take the values for x which satisfy BOTH inequalities.


{{{18+x>2x-3}}}
{{{18+3>x}}}
{{{21>x}}}


Do one more just to be certain.
{{{18+2x-3>x}}}
{{{18+x-3>0}}}
{{{x>-15}}}, which is not very meaningful.


The <b>intersection</b> of all three solutions is {{{highlight(x>21)}}}.


Side number 2 would be 2x-3 for x>21,
{{{2*21-3}}}, which is 39 at its limit.