Question 174309
{{{abs(4x-3)>5}}} means that {{{4x-3>5}}} or {{{-(4x-3)>5}}}, so:



Solve:  {{{4x-3>5}}} → {{{4x>8}}} → {{{x>2}}}



OR


Solve:  {{{-(4x-3)>5}}} &#8594; {{{-4x+3>5}}} &#8594; {{{-4x>2}}} (remember to reverse the sense of the inequality when multiplying both sides by a number less than zero) &#8594; {{{x<1/2}}}


Therefore any number that is either less than {{{1/2}}} or greater than {{{2}}} is in the solution set of {{{abs(4x-3)>5}}}.  In set builder notation:


{All x | x is real and (x < ½ or x > 2)}