Final answer:
To determine which of the following values is negative when (x+6)(x-5)<0, we first set each factor equal to zero and solve the equations. Then, we choose test points in each interval to determine the sign of the expression. The values of x that make the expression negative are x<-6 and -5
Step-by-step explanation:
To determine which of the following values is negative when (x+6)(x-5)<0, we need to find the values of x that make the expression less than zero.
We can start by setting each factor equal to zero: x+6=0 and x-5=0.
Solving these equations, we find that x=-6 and x=5.
To determine the sign of the expression between these values, we can choose a test point in each interval. For example, if we choose x=-7 (a value less than -6), the expression becomes (-7+6)(-7-5)=-1(2)=-2, which is negative.
If we choose x=0 (a value between -6 and 5), the expression becomes (0+6)(0-5)=6(-5)=-30, which is also negative.
Therefore, the values of x that make the expression negative are x<-6 and -5<x<5.