Question

solve the inequality and graph the solution.
1 + 3n ≥ -2
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 1 from both sides

$$1 + 3n-1\geq - 2-1$$
$$3n\geq - 3$$

Step2: Divide both sides by 3

$$\frac{3n}{3}\geq\frac{-3}{3}$$
$$n\geq - 1$$

To graph \(n\geq - 1\), we plot a closed - endpoint at \(n = - 1\) (because the inequality is \(\geq\)) and draw a ray to the right.

Answer:

The solution of the inequality \(1 + 3n\geq - 2\) is \(n\geq - 1\). On the number line, we have a closed circle at \(-1\) and a ray extending to the right.