the product of two numbers is negative only if one is positive and one negative
a... b......a*b
+....+........+
+....-.........-
-.....+.......-
-.....-........+
when the signs are the same the product is positive ... so the only way it can be negative on the interval that each factor is different sign..
(x +8)(x - 5) < 0
(x + 8) < 0 when x < -8
(x + 8) > 0 when x > -8
(x - 5) < 0 when x < 5
(x -5 ) > 0 when x > 5
x < -8 and x > 5 impossible
or
x > -8 and x < 5 happens when -8 < x < 5
so f(x) is decreasing on the interval is ( -8, 5)
use open brackets because the -8 and 5 are not in the answer
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the f function is increasing when both signs are the same
(x + 8) < 0 when x < -8
(x + 8) > 0 when x > -8
(x - 5) < 0 when x < 5
(x -5 ) > 0 when x > 5
x < -8 and x < 5
this means x < -8 makes both equations true
so the interval is (- inf , -8)
or
x > -8 and x > 5
x > 5 makes both equations true
this interval is ( 5 , infinity)
thats how you solve all those equations
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remember when BOTH inequalities have to be a certain value you have to use the LOGIC AND
THAT is why i said x>8 and x > -5 had to be true..
since anything x>8 makes both of these true that is the simple formula... for that combined one..