Question

express the interval shown on the number line in interval notation.
number line image with -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, open circles at -5 (between -6 and -4) and 1 (between 0 and 2)
answer attempt 1 out of 2
buttons: , ( ), ), ( , -∞, ∞, ∪, <, >, ≤, ≥, or
interval notation: blank box

Explanation:

Step1: Identify the endpoints

The number line has open circles at -5 (wait, looking at the number line: the first open circle is at -5? Wait, the marks are -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. Wait, the first open circle is between -6 and -4, so at -5? Wait no, the distance between -6 and -4 is 2 units, so each tick is 1 unit? Wait, -12, -10 (2 units), -8 (2), -6 (2), -4 (2), -2 (2), 0 (2), 2 (2), etc. Wait, no, maybe each tick is 1 unit. Wait, the first open circle is at -5? Wait, no, the labels are -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. So between -6 and -4, the middle is -5? Wait, no, the open circle is at -5? Wait, no, the first open circle is at -5? Wait, no, looking at the number line: the first open circle is at -5? Wait, no, the labels are -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. So the first open circle is at -5? Wait, no, the distance from -6 to -4 is 2, so each tick is 1. So -6, -5, -4: the open circle is at -5? Wait, no, the user's number line: the first open circle is at -5? Wait, no, the original number line: the first open circle is at -5? Wait, no, let's check again. The number line has arrows, open circles at -5? Wait, no, the labels are -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. So between -6 and -4, the open circle is at -5? Wait, no, maybe the first open circle is at -5? Wait, no, the second open circle is at 1? Wait, no, the second open circle is at 1? Wait, no, the labels are 0 and 2, so between 0 and 2, the open circle is at 1? Wait, no, the number line: the first open circle is at -5 (between -6 and -4), the second at 1 (between 0 and 2)? Wait, no, maybe the first open circle is at -5? Wait, no, let's see the intervals. The number line has two open intervals: one to the left of -5 (open circle) and one to the right of 1 (open circle)? Wait, no, the green line is from the left open circle (at -5) to the right open circle (at 1)? Wait, no, the green line is between the two open circles? Wait, no, the number line: the arrow is left, then a green line from the left open circle (at -5) to the right open circle (at 1)? Wait, no, the open circles are at -5 and 1? Wait, no, the labels: -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. So the first open circle is at -5 (between -6 and -4), the second at 1 (between 0 and 2). Wait, no, maybe the first open circle is at -5? Wait, no, the distance between -6 and -4 is 2, so each tick is 1. So -6, -5, -4: open circle at -5. Then 0, 1, 2: open circle at 1. Wait, but the green line is between these two open circles? Wait, no, the green line is from the left open circle (at -5) to the right open circle (at 1)? Wait, no, the number line: the green line is between the two open circles, so the interval is from -5 (open) to 1 (open). Wait, no, let's check again. The number line: the first open circle is at -5 (between -6 and -4), the second at 1 (between 0 and 2). So the interval is (-5, 1)? Wait, no, maybe I misread. Wait, the first open circle is at -5? Wait, no, the labels are -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. So the first open circle is at -5? Wait, no, the distance from -6 to -4 is 2, so each tick is 1. So -6, -5, -4: open circle at -5. Then 0, 1, 2: open circle at 1. So the interval is (-5, 1)? Wait, no, maybe the first open circle is at -5 and the second at 1, so the interval is (-5, 1). Wait, but let's confirm: open circles mean the endpoints are not included, so we use parentheses. So the interval is from -5 to 1, not including -5 and 1. So interval notation is (-5, 1). Wait, but maybe I made a mistake. Wait, the first open circle is at -5? Wait, no, the number line: the first open circle is at -5? Wait, no, the labels are -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12. So between -6 and -4, the open circle is at -5. Between 0 and 2, the open circle is at 1. So the interval is (-5, 1).

Step2: Write the interval notation

Since both endpoints are open (not included), we use parentheses. So the interval is $(-5, 1)$.

Answer:

$(-5, 1)$