Question

choose the inequality that represents the following graph.

choose 1 answer:
a ( x < 0 )
b ( x leq 0 )
c ( x > 0 )
d ( x geq 0 )

Explanation:

To determine the inequality from the number - line graph:

1. First, observe the point on the number - line. The dot at 0 is a closed (filled - in) dot. A closed dot on a number - line graph for an inequality means that the value at that point (0 in this case) is included in the solution set.
2. Then, observe the direction of the arrow. The arrow is pointing to the right, which means that we are including all numbers greater than or equal to 0.

• For option A ($x < 0$), the graph would have an open dot at 0 and an arrow to the left, so it is incorrect.
• For option B ($x\leq0$), the graph would have a closed dot at 0 and an arrow to the left, so it is incorrect.
• For option C ($x > 0$), the graph would have an open dot at 0 and an arrow to the right, so it is incorrect.
• For option D ($x\geq0$), it has a closed dot at 0 (indicating that 0 is included) and an arrow to the right (indicating numbers greater than 0 are included), which matches the given graph.

Answer:

D. $x\geq0$