Question

match the inequality below to the correct graph.
$6 \leq x$
a <----|----|----|----|---->
-10 -5 0 5 10
(blue dot at 5, arrow to right)

b <----|----|----|----|---->
-10 -5 0 5 10
(open circle at 5, arrow to left)

c <----|----|----|----|---->
-10 -5 0 5 10
(blue dot at 5, arrow to left)

d <----|----|----|----|---->
-10 -5 0 5 10
(open circle at 5, arrow to right)

Explanation:

Step1: Analyze the inequality

The inequality is \(6 \leq x\) (wait, no, looking at the number lines, the key number is 5? Wait, maybe a typo, but the inequality is \(5 \leq x\)? Wait, the number lines have 5 as a mark. Let's re-express: the inequality is \(5 \leq x\) (since the number lines have 5). So \(x \geq 5\).

For a number line graph of \(x \geq 5\): we need a closed circle at 5 (because it's "less than or equal" or "greater than or equal" – here \(x \geq 5\) means 5 is included) and the arrow pointing to the right (since x is greater than or equal to 5, so values to the right of 5).

Step2: Evaluate each option

• Option A: Closed circle at 5, arrow to the right. This matches \(x \geq 5\).
• Option B: Open circle at 5, arrow to the left. Doesn't match.
• Option C: Closed circle at 5, arrow to the left. Doesn't match (arrow left is for \(x \leq 5\)).
• Option D: Open circle at 5, arrow to the right. Doesn't match (open circle means 5 is not included, but we need closed for "equal").

Answer:

A. The graph with a closed circle at 5 and an arrow pointing to the right.