Question

which graph matches the inequality k < 3?
a)
←
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
7
b)
←
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
7
c)
←
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
7
d)
←
−7
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
7

Explanation:

Step1: Analyze the inequality \( k < 3 \)

For a number line graph of \( k < 3 \), the point at 3 should be an open circle (since \( k \) is not equal to 3) and the arrow should point to the left (since we want values less than 3).

Step2: Evaluate each option

• Option A: Open circle at 3, arrow to the left (values less than 3). This matches \( k < 3 \).
• Option B: Open circle at 3, arrow to the right (values greater than 3). Does not match.
• Option C: Closed circle at -3, arrow to the left. Does not match \( k < 3 \) (wrong point and closed circle).
• Option D: Closed circle at 3, arrow to the right. Does not match (closed circle and wrong direction).

Answer:

A. The graph with an open circle at 3 and an arrow pointing to the left (values less than 3)