Question 1023998
abs(2x-5)/5=9


{{{abs(2x-5)/5=9}}}


Solve first for the absolute value.
{{{(5/1)(abs(2x-5)/5)=(5/1)*9}}}


{{{abs(2x-5)=45}}}


Review the definition of absolute value on your own, paying attention to both the described meaning AND the graphical meaning on a number line.


Your equation now has two conditions to solve for.


EITHER  {{{2x-5=45}}}   OR   {{{-(2x-5)=45}}}.
The first one is for the condition of 2x-5 being non-negative; and the second one is for the condtion of 2x-5 being negative.


First one,
{{{2x=45+5}}}
{{{2x=50}}}
{{{x=25}}}


Second one,
{{{-2x+5=45}}}
{{{-2x=45-5}}}
{{{-2x=40}}}
{{{x=-20}}}


ANSWER:  x is 25 or -20.