\[{x}^{2}-3x-4>0\]
1
因數x2−3x−4{x}^{2}-3x-4。
(x−4)(x+1)>0(x-4)(x+1)>0

2
求解xx。
x=4,−1x=4,-1

3
從上面xx的值，我們要測試這3個區間。
x<−1−1<x<4x>4\begin{aligned}&x<-1\\&-1<x<4\\&x>4\end{aligned}

4
在每個區間選擇一個測試點。
For the interval x<−1x<-1:

Let's pick x=−2x=-2. Then, (−2)2−3×−2−4>0{(-2)}^{2}-3\times -2-4>0.
After simplifying, we get 6>06>0, which is
true
.
保留此區間
.

For the interval −1<x<4-1<x<4:

Let's pick x=0x=0. Then, 02−3×0−4>0{0}^{2}-3\times 0-4>0.
After simplifying, we get −4>0-4>0, which is
false
.
刪除此區間
.

For the interval x>4x>4:

Let's pick x=5x=5. Then, 52−3×5−4>0{5}^{2}-3\times 5-4>0.
After simplifying, we get 6>06>0, which is
true
.
保留此區間
.

5
因此，
x<−1,x>4x<-1,x>4

完成
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