Question

graph the solution to the following inequality on the number line.
(x - 1)(x + 6)>0

Explanation:

Step1: Find the roots

Set $(x - 1)(x + 6)=0$. Then $x-1 = 0$ gives $x = 1$ and $x+6=0$ gives $x=-6$.

Step2: Analyze intervals

We have three intervals to consider: $x<-6$, $-6 1$.
For $x<-6$, let $x=-7$. Then $(-7 - 1)(-7 + 6)=(-8)\times(-1)=8>0$.
For $-6For $x>1$, let $x = 2$. Then $(2 - 1)(2 + 6)=1\times8 = 8>0$.

Answer:

The solution is $x<-6$ or $x>1$. On the number - line, we have an open - circle at $x=-6$ and shade to the left, and an open - circle at $x = 1$ and shade to the right.