Question 898344
Part of your inequality as given is unclear.  I will assume you intend the fraction as a separate factor:  {{{(1/7)abs(4z+5)+2>5}}}


Simplify up to the absolute value function.
{{{abs(4z+5)>(5-2)*7}}}
{{{abs(4z+5)>21}}}


Now solve for each of two different cases.


4z+5 may be positive or negative or zero.


{{{highlight_green(4z+5>=0)}}}:
{{{4z+5>21}}}
{{{4z>16}}}
{{{z>16/4}}}
{{{z>4}}}


{{{highlight_green(4z+5<0)}}}:
{{{-4z-5>21}}}
{{{-4z>21+5}}}
{{{-4z>26}}}
CAREFUL HERE....
{{{z<26/(-4)}}}
{{{z<-13/2}}}


Put together, the solution for z is
{{{highlight(z<-13/2)}}}  <b>OR</b>  {{{highlight(z>4)}}}