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 \(x \geq 0\).

Step2: Determine the ray properties

For the inequality \(x \geq 0\), the endpoint is at \(x = 0\) and it is a closed circle (because the inequality is "greater than or equal to", so the endpoint is included). The direction of the ray should be to the right (since \(x\) is greater than or equal to 0, we shade to the right of 0). Among the given rays, the ray with a closed circle and pointing to the right (the second ray: \(\boldsymbol{\bullet
ightarrow}\)) should be selected and placed at 0 on the number line.

Answer:

To graph \(x \geq 0\), use the closed - circle (filled dot) ray pointing to the right (\(\bullet
ightarrow\)) and place its endpoint at \(0\) on the number line.