Question 933499
<i>The difference between 9 and 3 times the distance between x and -5 is greater than 6. </i>



{{{9-3*abs(x-(-5))>6}}}
{{{9-3*abs(x+5)>6}}}


Continue simplifying.
{{{-3*abs(x+5)>6-9}}}
{{{-3*abs(x+5)>-3}}}
Multiplying both sides by a negative quantity will reverse the inequality direction:
{{{(-1/3)(-3*abs(x+5))<(-1/3)(-3)}}}
{{{highlight_green(abs(x+5)<1)}}}



x+5 could be negative or non-negative.  Solve for each case.


Non-negative,
{{{x+5<1}}}
{{{x<-4}}}
If negative,
{{{-x-5<1}}}
{{{x+5>-1}}}
{{{x>-1-5}}}
{{{x>-6}}}
-
Put those two results together.
{{{highlight(-6<x<-4)}}}


The meaning of absolute value is how far from 0 on the number line.  For more detailed explanations and study, use your textbook.  Absolute Value is always a POSITIVE quantity.