Question

choose the inequality that represents the following graph.

number line with a closed dot at 1 and arrow pointing to the right

choose 1 answer:

a ( x < 1 )

b ( x leq 1 )

c ( x > 1 )

d ( x geq 1 )

Explanation:

Step1: Analyze the graph's dot

The dot at 1 is filled (closed), which means 1 is included in the solution set. So the inequality should have a "greater than or equal to" or "less than or equal to" sign with 1.

Step2: Analyze the graph's direction

The arrow is pointing to the right, which means the values are greater than 1 (including 1, because the dot is closed). So the inequality should be \( x \geq 1 \)? Wait, no, wait. Wait, the closed dot at 1 and the arrow to the right means all numbers greater than or equal to 1? Wait, no, wait, let's check again. Wait, the number line: the dot is at 1, and the blue line is to the right of 1 (including 1, since the dot is closed). So the solution is \( x \geq 1 \)? Wait, but let's check the options. Option D is \( x \geq 1 \). Wait, but let's confirm the dot: closed dot means the endpoint is included. So if the arrow is to the right, starting at 1 (included), then \( x \geq 1 \). Wait, but let's check the options again. Option D is \( x \geq 1 \), option B is \( x \leq 1 \) (arrow to the left), option A is \( x < 1 \) (open dot, arrow left), option C is \( x > 1 \) (open dot, arrow right). So the graph has a closed dot at 1 and arrow to the right, so it's \( x \geq 1 \), which is option D. Wait, no, wait, maybe I made a mistake. Wait, the number line: the dot is at 1, and the blue line is from 1 to the right. So the values are 1, 2, 3, etc. So that's \( x \geq 1 \), which is option D.

Answer:

D. \( x \geq 1 \)