1. ## Solving Inequality

Hello Everyone,

I have a very embarrassing question. I'm studying the introduction chapter in my Calculus book.

I have the following problem: $\displaystyle (x+2)(x-1)(x-3) > 0$

The answer in my book: $\displaystyle (-2,1)\cup(3,8)$

My answer doesn't match and I can't really figure out why:

$\displaystyle (x+2)(x-1)(x-3) > 0$

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 $\displaystyle (-2,1) \cup (3,\infty)$

2. ## 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.

3. ## Re: Solving Inequality

proceed like this to consider remaining cases