Answer:
The solution set is { x | x -2 or x
1}
Step-by-step explanation:
The given inequality is
Let us factor
so we have
Let us find zeros of
or
or
so we have intervals (-∞ , -2) , (-2 , 1) and (1, ∞)
we need to find in which interval is is greater than 0
so we will assume the value of x in each interval and will plug it in and will check if we get negative or positive value
Let us check the sign of in (-∞ , -2)
we can take x=-3 and plug it in
so we have
( which is greater than 0)
This shows (-∞, -2) is one of the solution set
similarly we can check the sign of in (-2,1)
we take x= 0 , so we have
( which is less than 0)
This shows (-2,1) is not the solution set
now we check the sign of in (1 ,∞)
we can assume x= 2, so we have
( which is greater than 0)
This shows (1 ,∞) is the solution set
Hence the solution set in interval notation (∞ ,-2)∪(1,∞)
we can write this as { x | x -2 or x
1}
