Question 671969
First, you have to recognize what it is
It's an INequality.
There are 4 types of inequalities
> means greater than
< means less than
>= means greater than or equal to
<= means less than or equal to
----------------------------
The plain old = means equal to
Your inequality is
{{{ 5n + 3 - 4n < -5 - 3n }}}
This says that the left side is less than the 
right side. There is 1 unknown, {{{n}}}, in this inequality
----------------------------
The basic rule with inequalities is the same as
when you just have an = sign.
Whatever you do to one side, you must do the exact
same thing to the other side
------------------------
First, I'm going to subtract {{{3}}} from both sides
{{{ 5n + 3 - 3 < -5 -3 - 3n }}}
{{{ 5n < -8 - 3n }}}
Now I will add {{{ 3n }}} to both sides
{{{ 5n + 3n < -8 - 3n + 3n }}}
{{{ 8n < -8 }}}
Divide both sides by {{{ 8 }}}
{{{ (8/8)*n < (-8/8) }}}
{{{ n < -1 }}}
-----------
Notice that the < sign never changed, and
it usually does not.
-----------
There is very simple way to check the work.
I am saying that {{{n}}} is less than {{{-1}}},
so I will say that {{{ n = -1.01 }}} which is
slightly less than {{{ -1 }}}
{{{ 5n + 3 - 4n < -5 - 3n }}}
{{{ 5*(-1.01) + 3 - 4*(-1.01) < -5 - 3*(-1.01) }}}
{{{ -5.05 + 3 + 4.04 < -5 + 3.03 }}}
( note that minus x minus = plus )
{{{ + 3 - 1.01 < -5 + 3.03 }}}
{{{ -1.99 < -1.97 }}}
This is true, so I think my solution is correct
--------------
Hope this helps