Question 637056
you must split the equation into its two possible two cases to clear absolute value bars, one case for each sign:

1.

    {{{(t-8) = 2}}}-----or-----{{{-(t-8)=2}}} 
    {{{t-8 = 2}}}-----or-----{{{-t+8=2}}}
    {{{t =10 }}}-----or-----{{{8-2=t}}}  
    -----------------or      {{{t=6}}}

Then the solution is {{{t}}} = {{{10}}}, {{{6}}}.

2.

   {{{(2x+5) =7}}}-----or-----{{{-(2x+5)=7}}} 
    {{{2x=7-5}}}-----or-----{{{-2x-5=7}}}
    {{{2x =2 }}}-----or-----{{{-2x=7+5}}} 
{{{x =1 }}}-----or-----{{{-2x=12}}}
  -------------------or      {{{x=-6}}}



Then the solution is {{{x}}} = {{{1}}}, {{{-6}}}.