
Solving Inequality
Hello Everyone,
I have a very embarrassing question. I'm studying the introduction chapter in my Calculus book(Worried).
I have the following problem: $\displaystyle (x+2)(x1)(x3) > 0$
The answer in my book: $\displaystyle (2,1)\cup(3,8)$
My answer doesn't match and I can't really figure out why:
$\displaystyle (x+2)(x1)(x3) > 0$
Split points: 2, 1, 3
There must be four intervals to test $\displaystyle (\infty,2), (2,1), (1,3), and(3,\infty)$
So I use the following test points to determine when the inequality is greater than 0: 3, 0, 2, 4
x= 3 [] Doesn't Work
x = 0 [+] Does Work
x = 2 [] Doesn't Work
x = 4 [+] Does Work
So according to me and this work I did the solution should be $\displaystyle (2,1) \cup (3,\infty)$

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Re: Solving Inequality
Hi,
Text books are not infallible; in this case you're right and the book is wrong. I'm very prone to arithmetic and algebraic errors, so I almost always check my calculations for such problems by drawing a graph with my graphing software. I suggest you do the same.
Attachment 29100

1 Attachment(s)
Re: Solving Inequality
Attachment 29101proceed like this to consider remaining cases