The inequality is .
The changed expression is .
The condition is .
Consider the inequality .
Let .
The zeros of are at
and
.
The zeros of are at
and
.
Draw a sign chart by using the values and
.
Note : The hallow circle denote that the value are excluded in the solution set.
\Observe the sign chart :
\The set of value of denoted in pink color represents the solution set.
The solutions of are
values such that
is negitive.
From the sign chart the solution set is .
\
Now consider the changed expression .
If the left side of the expression is multiplied by , the zeros will remain the same but the sign of the expression will change for each interval.
Note : The hallow circle denote that the value are excluded in the solution set.
\Observe the sign chart :
\The set of value of denoted in pink color represents the solution set.
Thus, the zeros will remain the same but the solution set will consist of all numbers outside of the original solution set.
\Therefore the new solution set of new inequality is .
From the sign chart the solution set is .
The solution set of is
.