Question

solve the inequality and graph the solution.
2v + 7 ≥ -5
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it:

Explanation:

Step1: Subtract 7 from both sides

$$\begin{align*} 2v+7 - 7&\geq - 5-7\\ 2v&\geq - 12 \end{align*}$$

Step2: Divide both sides by 2

$$\begin{align*} \frac{2v}{2}&\geq\frac{-12}{2}\\ v&\geq - 6 \end{align*}$$

To graph the solution:

• Plot a closed endpoint at \(v = - 6\) (because the inequality is \(\geq\), so the endpoint is included).
• Draw an arrow to the right (since \(v\) is greater than or equal to \(-6\)).

Answer:

The solution of the inequality \(2v + 7\geq - 5\) is \(v\geq - 6\). On the number - line, we have a closed circle at \(-6\) and a ray extending to the right.