Let's go through each problem step-by-step using the provided clues and answer them accordingly.
1. What is 3 to the left of 0 ?
To find 3 units to the left of 0 on a number line, move 3 units in the negative direction from 0. This places us at:
[tex]\[
0 - 3 = -3
\][/tex]
Answer: [tex]$-3$[/tex]
2. What is 5 to the right of -1 ?
To find 5 units to the right of -1, move 5 units in the positive direction from -1. This places us at:
[tex]\[
-1 + 5 = 4
\][/tex]
Answer: [tex]$4$[/tex]
3. What is 3 to the left of 2 ?
To find 3 units to the left of 2, move 3 units in the negative direction from 2. This places us at:
[tex]\[
2 - 3 = -1
\][/tex]
Answer: [tex]$-1$[/tex]
4. What is 6 to the right of -5 ?
To find 6 units to the right of -5, move 6 units in the positive direction from -5. This places us at:
[tex]\[
-5 + 6 = 1
\][/tex]
Answer: [tex]$1$[/tex]
5. [tex]$-12 + 7 = ?$[/tex]
Adding 7 to -12 involves moving 7 units to the right from -12 on the number line. This gives:
[tex]\[
-12 + 7 = -5
\][/tex]
Answer: [tex]$-5$[/tex]
6. [tex]$1 + -3 = ?$[/tex]
To add -3 to 1, move 3 units to the left from 1 on the number line. This gives:
[tex]\[
1 + (-3) = -2
\][/tex]
Answer: [tex]$-2$[/tex]
7. [tex]$-6 + 6 = ?$[/tex]
Adding 6 to -6 means moving 6 units to the right from -6 on the number line. This brings us directly to 0.
[tex]\[
-6 + 6 = 0
\][/tex]
Answer: [tex]$0$[/tex]
8. [tex]$-1 + -1 = ?$[/tex]
Adding -1 to -1 means moving 1 unit to the left from -1 on the number line. This places us at:
[tex]\[
-1 + (-1) = -2
\][/tex]
Answer: [tex]$-2$[/tex]
9. [tex]$7 + -2 = ?$[/tex]
Adding -2 to 7 involves moving 2 units to the left from 7. This results in:
[tex]\[
7 + (-2) = 5
\][/tex]
Answer: [tex]$5$[/tex]
10. [tex]$-10 + -5 = ?$[/tex]
Adding -5 to -10 means moving 5 units to the left from -10 on the number line. This places us at:
[tex]\[
-10 + (-5) = -15
\][/tex]
Answer: [tex]$-15$[/tex]
11. The temperature was [tex]$-2^{\circ} F$[/tex]. Then it dropped 2 degrees. What was the temperature then?
Initially, the temperature is [tex]$-2^{\circ} F$[/tex]. If it drops by 2 degrees, subtracting 2 degrees from -2 results in:
[tex]\[
-2 - 2 = -4
\][/tex]
Answer: [tex]$-4^{\circ} F$[/tex]
12. To add -4 to 5 on a number line, start at +5 and move 4 spaces to the [tex]$\qquad$[/tex]
When adding -4 to 5, you start at 5 and move 4 units to the left on the number line, hence:
[tex]\[
5 - 4 = 1
\][/tex]
Answer: left
