Question

solve the inequality and graph the solution. 2(v + 7) ≥ 8. plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

$2(v + 7)=2v+14$, so the inequality becomes $2v + 14\geq8$.

Step2: Subtract 14 from both sides

$2v+14 - 14\geq8 - 14$, which simplifies to $2v\geq - 6$.

Step3: Divide both sides by 2

$\frac{2v}{2}\geq\frac{-6}{2}$, so $v\geq - 3$.

To graph the solution on the number - line:

• The endpoint is at $v=-3$. Since the inequality is $\geq$, the endpoint is a closed circle.
• The solution includes all values greater than or equal to $-3$, so we draw a ray starting at $-3$ and going to the right.

Answer:

The solution of the inequality is $v\geq - 3$. On the number - line, there is a closed circle at $-3$ and a ray extending to the right.