Question 421195
if, for each of the factors, you divide both sides of the equation by the other 2 factors, you will wind up with:


x + 2 > 0
x - 17 > 0
x + 1 > 0


this leads to:


x > -2
x > 17
x > -1


let x = 18 (> 17):


this leads to (18+2)*(18-17)*(18+1) > 0 which leads to:
20*1*19 > 0 which is true, so we know that if x > 17, the equation will be true.


let x = 0 (> -1)


this leads to (0+2)*(0-17)*(0+1) > 0 which leads to:
2*-17*1 > 0 which is false, so we know that if x > -1, the equation will be false.


let x = -1.5 (> -2, but not > -1)


this leads to:


(-1.5+2)*(-1.5-17)*(-1.5+1) which leads to:
.5*-18.5*-.5 > 0 which is true, so we kno that if x > -2 but not greater than -1, the equation will be true.


looks like the equation is true when x > 17 or when x > -2 but not greater than -1.


note that x cannot be equal to -1, -2, or 17 because then the equation will be equal to 0 which is not > 0.


your answer will therefore have to be:


(x+2) * (x-17) * (x+1) > 0 when x > 17 or -2 < x < -1


graph of the equation looks like this:


{{{graph(1200,600,-5,25,-100,40,(x+1)*(x+2)*(x-17))}}}


you can see from the graph that the equation is > 0 during the intervals indicated.


solving this does require to pick values for x that are consistent with what the eqution is indicating.


x > 17 leads to x = 18 or any other value greater than 17
x > -1 leads to x = 0 or any other value greater than -1
x > -2 leads to x = -1.5 or any other value greater than -2 but not greater than 1.


you also have to keep in mind that x cannot equal -2, -1, or 17, because then the equation will be equal to 0 which is not greater than 0.