Question 406080
Hi,

  I'll explain this problem with a more simple problem that shows
the exact same idea.
{{{1 > -x}}}
OK, what you want to find is {{{x}}}. What is the given inequality telling you?
If {{{x = 1}}}
then {{{1 > -1}}} true
-----------------
If {{{x = 0}}}
then {{{1 >0}}} true
-----------------
If {{{x = -1}}}
then {{{1 > 1}}} not true
----------------
In fact, if {{{x}}} is -1, -2, -3, -4, or any minus number more negative than {{{-1}}},
the inequality is not true. It is true for any number that is more positive than {{{-1}}}
That includes the negative fractions like -1/3, -1/4, -1/5, etc. and also the 
positive fractions like 1/3, 1/4, etc. and then it is true for all the positive numbers,
1, 2, 3, 4, etc.
--------------
Now I still want to find {{{x}}}. The normal way to do this with an equality is to
divide both sides by {{{-1}}}
{{{1/(-1) > (-x)/(-1)}}}
plus divided by minus is minus and
minus divided by minus is plus, so
{{{-1 > x}}}
and now just write this going from right to left
{{{x < -1}}} this is the same thing
But what happened? I said the original inequality was true for all numbers
greater than {{{-1}}}, or, in other words, {{{x > -1}}}. 
Now I divided both sides by {{{-1}}}, and the result is telling me just the opposite.
This leads to a general rule:
------------------------------------------------------
Whenever you divide both sides of an inequality by a minus quantity,  
you must reverse the inequality sign when you are done.
Following this law:
{{{1 > -x}}}
{{{1/(-1) < (-x)/(-1)}}}
{{{-1 < x}}} 
Now rewriting this from right to left:
{{{x > -1}}}
Notice I reversed the inequality sign, and it is now true.
----------------
So, to solve your problem:
{{{2 < -8s}}}
{{{2/(-1) > (-8/-1)*s}}} (I reversed the inequality sign)
{{{-1/4 > s}}}
{{{s < -1/4}}} (I just rewrote it going right to left)
This is true- try any number that is greater than or equal to {{{-1/4}}},
and the inequality becomes false.
for example:
{{{s = -1/10}}}
{{{2 < -8*(-1/10)}}}
{{{20 < 8/10}}} not true
----------------
I hope all this helps and isn't too confusing.