Question

graph the solution of the inequality.
1 ≤ x + 1
first select the ray that matches the endpoint (open or closed) and direction (left or right) that you want. then select the location on the number line where you want the endpoint to be located.
-3 -2 -1 0 1 2 3

Explanation:

Step1: Solve the inequality

Subtract 1 from both sides of the inequality \(1 \leq x + 1\). We get \(1-1\leq x + 1-1\), which simplifies to \(0\leq x\) or \(x\geq0\).

Step2: Determine the ray properties

For the inequality \(x\geq0\), the endpoint is at \(x = 0\) and since the inequality is "greater than or equal to", the endpoint is closed (filled circle). The direction of the ray should be to the right (since \(x\) is greater than or equal to 0, we include all numbers from 0 to the right on the number line). So we select the ray with a closed endpoint (the one with the filled circle) pointing to the right and place the endpoint at 0 on the number line.

Answer:

To graph \(x\geq0\), use the ray with a closed endpoint (filled circle) pointing to the right, with the endpoint located at 0 on the number line.