Question

solve for x and graph the solution.
5(x - 1)(x - 6) > 0
plot the endpoints. select an endpoint to change it from closed to open. select the a segment, ray, or line to delete it.

Explanation:

Step1: Find the roots

Set $5(x - 1)(x - 6)=0$. Then $x-1 = 0$ or $x - 6=0$, so $x=1$ and $x = 6$ are the roots.

Step2: Test intervals

Consider the intervals $(-\infty,1)$, $(1,6)$ and $(6,\infty)$.
For $x=0$ (in the interval $(-\infty,1)$), $5(0 - 1)(0 - 6)=5\times(- 1)\times(-6)=30>0$.
For $x = 3$ (in the interval $(1,6)$), $5(3 - 1)(3 - 6)=5\times2\times(-3)=-30<0$.
For $x=7$ (in the interval $(6,\infty)$), $5(7 - 1)(7 - 6)=5\times6\times1 = 30>0$.

Step3: Determine solution

The inequality $5(x - 1)(x - 6)>0$ is satisfied for $x<1$ or $x>6$.

Answer:

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