Question

(x+16)(x-19)(x+6)>0

Answer 1

so solve it to find the values that fit the inequality?

Answer 2

yes

Answer 3

we know this is a polynomial equation and the zeros of the equation are -16, -6, and 19. we find where this equation is greater than zero by plugging in values for the intervals (-infinity,-16), (-16,-6), (-6,19), and (19, infinity)

Answer 4

so how is that written?

Answer 5

yup, for each interval (-infinity,-16), (-16,-6), (-6,19), and (19, infinity), check the signs of the linear factors, and the sign of the overall polynomial.
For example, in the interval (-infinity,-16) all 3 linear factors are negative, and thus the whole polynomial is negative because 3 negative numbers multiplied together is a negative number, therefore values of x less than 16 are not solutions of the equations.
however, for the interval (-16,-6), x+16 is positive and the two other linear factors x-19 and x+6 are negative. A positive number multiplied by 2 negative numbers is a positive number, and therefore satisfies the inequality. Thus, values of x between -16 and -6 are solutions to the inequality. Continue with the other intervals, and summarize your solutions.

Answer 6

so my answer is {x>19}

Answer 7

you have to include all the intervals where the equation is positive. so, you answer would be {-16<x<-6}U{x>19}