Question

graph the solution to this inequality on the number line.
-2 + x ≥ 1
number line from -5 to 5
options:
the circle will be open going to the right on 3
the circle will be closed going to the left on 3
the circle will be closed going to the right on 3
the circle will be open going to the left on 3

Explanation:

Step1: Solve the inequality

Start with the inequality \(-2 + x \geq 1\). Add 2 to both sides to isolate \(x\):
\(x \geq 1 + 2\)
\(x \geq 3\)

Step2: Analyze the number line graph

• For the inequality \(x \geq 3\), the boundary point is \(3\). Since the inequality is "greater than or equal to" (\(\geq\)), the circle at \(3\) should be closed (to include \(3\) in the solution).
• The solution \(x \geq 3\) means all values to the right of \(3\) (including \(3\)) are part of the solution, so the arrow points to the right.

Answer:

The circle will be closed going to the right on 3 (matching the second option: "The circle will be closed going to the right on 3").