Gregg O. answered • 10/06/15
Tutor
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Cal Poly Pomona engineering valedictorian, expert in geometry
This problem becomes easier when you see that to get a product greater than 0, both factors must either be positive or negative, and not equal to zero. Since setting either factor equal to 0 makes the entire expression on the left hand side of the inequality 0 which is not > 0, we must use < and > rather than ≤ or ≥ in finding our solutions.
Both factors greater than 0:
x-7> 0 and x+2 > 0
x>-7 and x > -2
The intersection of these inequalities is x>-2; when x>-2, both factors are positive and not equal to 0.
Both factors negative but not equal to 0:
x-7<0 and x+2 < 0
x<-7 and x < -2
The intersection of these inequalities is x<-7. The factors are both negative but not equal to 0 when x<-7.
The solution is the combination of these two posibilites using a logical or:
x<-7 or x>-2.
