Question

fill in the blanks to complete the equation that describes the diagram.
-9 -6 -3 0 3
-1+\square =\square

Explanation:

Step1: Analyze the number line movement

The first arrow starts at -1 (assuming the second dashed line is at -1? Wait, no, let's check the positions. Wait, the second dashed line is between -3 and 0, let's see the intervals. From -9 to -6 is 3 units, -6 to -3 is 3, -3 to 0 is 3, 0 to 3 is 3. So each tick is 1 unit? Wait, no, the marks are at -9, -6, -3, 0, 3. So between -9 and -6, there are two spaces, so each space is 1.5? Wait, no, maybe the second dashed line is at -1? Wait, the first dashed line (longer arrow) is at -7? Wait, no, let's re-examine. Wait, the equation is -1 + [blank] = [blank]. Let's see the movement. The first arrow (longer) goes from where? Wait, the second dashed line (shorter arrow) is at -1? Wait, no, the shorter arrow is at a position 1 unit left of 0? Wait, 0 is at the mark, so left of 0 is -1? Wait, no, the marks are at -9, -6, -3, 0, 3. So between -3 and 0, there are two intervals, so each interval is 1.5? Wait, no, maybe the shorter arrow is at -1 (since 0 -1 = -1), and the longer arrow is at -7? Wait, no, let's think about the addition. The first term is -1, then we add a negative number (since the arrow is left, which is negative direction). Let's see the distance between -1 and the final position. Wait, the longer arrow's dashed line: let's count the units. From -1 (shorter dashed line) to the longer dashed line: how many units left? Let's see the marks: -9, -6, -3, 0, 3. So from -1 to -7: that's 6 units left? Wait, no, -1 + x = y. Let's see, if the final position is -7, then -1 + x = -7 → x = -6. Wait, let's check the number line. The shorter arrow is at -1 (since it's 1 unit left of 0), and the longer arrow is at -7 (since from -6, left 1 unit is -7? Wait, the marks are at -9, -6, -3, 0, 3. So between -9 and -6: 3 units, -6 to -3: 3, -3 to 0: 3, 0 to 3: 3. So each major mark is 3 units apart, with two minor intervals in between, so each minor interval is 1 unit? Wait, -9, then -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3. Oh! Maybe the number line has marks at -9, -6, -3, 0, 3, but the minor ticks are at each integer. So -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3. So the shorter dashed line (shorter arrow) is at -1 (since it's 1 unit left of 0), and the longer dashed line (longer arrow) is at -7 (since -1 + (-6) = -7). Let's check: -1 + (-6) = -7. Yes, that makes sense. So the first blank is -6 (since we move 6 units left, which is adding -6), and the second blank is -7.

Step2: Verify the addition

-1 + (-6) = -7. Let's check: adding a negative number is subtracting its absolute value. So -1 -6 = -7. That matches the number line movement (moving 6 units to the left from -1 lands at -7).

Answer:

-6, -7 (so the equation is \(-1 + (-6) = -7\))