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: Test intervals

We have three intervals to test: $x<-6$, $-61$.
For $x<-6$, let $x=-7$. Then $(-7 - 1)(-7 + 6)=(-8)\times(-1)=8\geq0$, so this interval is part of the solution.
For $-6For $x>1$, let $x = 2$. Then $(2 - 1)(2 + 6)=1\times8 = 8\geq0$, so this interval is part of the solution.
Also, since the inequality is $\geq0$, the roots $x=-6$ and $x = 1$ are included in the solution.

Answer:

The solution is $x\leq - 6$ or $x\geq1$. On the number - line, we would have a closed circle at $x=-6$ and shade to the left, and a closed circle at $x = 1$ and shade to the right.