Question 421195: I am trying to solve this..I am confused
(x+2)(x-17)(x+1)>0
Found 2 solutions by Theo, Gogonati:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
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.
Answer by Gogonati(855)  (Show Source):
You can put this solution on YOUR website! Make a table to study the sign of the product of linear equations:
|-2 -1 |17
---|---|------|------|-----
x+2 - 0 + | + | +
---|---|-------------|-----
x+1| - | - 0 + | +
---|---|------|-----------
x-17 - | - | - 0 +
---|---|------|------|----
P. | - | + | - | +
---------------------------
Answer: From the table we conclude that for -2 < x < -1 and x > 17 the inequality is satisfy.
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