Question
When adding integers:
When subtracting integers, remember to add the opposite (Keep Change Change).
Now, determine ALL of the number(s) that will make the statement true. Numbers may be used more than once.
Desmos Scientific Calculator (To open the calculator in a new window, remember to hold Ctrl before selecting this link.)
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
___ + 8 = 0 -6 + ___ = negative number ___ - (-8) = positive number
When subtracting integers, remember to add the opposite (Keep Change Change).
Now, determine ALL of the number(s) that will make the statement true. Numbers may be used more than once.
Desmos Scientific Calculator (To open the calculator in a new window, remember to hold Ctrl before selecting this link.)
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
___ + 8 = 0 -6 + ___ = negative number ___ - (-8) = positive number
Answers
GPT-4o mini
To solve each equation:
1. **For \( \_\_ + 8 = 0 \):**
To find the number that, when added to 8, equals 0, we can set up the equation:
\[
x + 8 = 0
\]
Subtracting 8 from both sides gives:
\[
x = -8
\]
So, the response here is **-8**.
2. **For \( -6 + \_\_ = \text{negative number} \):**
The left-hand side of this equation must yield a negative number. We can rewrite it to find the conditions for this to be true:
\[
-6 + x < 0
\]
Adding 6 to each side results in:
\[
x < 6
\]
Thus, **any number less than 6** will satisfy this condition. Examples include **-7, -6, -5, 0, etc.**
3. **For \( \_\_ - (-8) = \text{positive number} \):**
We can simplify this to \( x + 8 \) since subtracting a negative is the same as adding a positive:
\[
x + 8 > 0
\]
Subtracting 8 from each side gives:
\[
x > -8
\]
Thus, **any number greater than -8** will satisfy this condition. Examples include **-7, 0, 1, 2, etc.**
To summarize:
- The answer for the first blank is **-8**.
- The second blank can be filled with any integer less than **6** (for example, **-7**).
- The third blank can be filled with any integer greater than **-8** (for example, **-7** as a valid response too).
If you need a clear specific response for each blank:
1. First box: **-8**
2. Second box: **-7** (or any number less than 6)
3. Third box: **-7** (or any number greater than -8)
1. **For \( \_\_ + 8 = 0 \):**
To find the number that, when added to 8, equals 0, we can set up the equation:
\[
x + 8 = 0
\]
Subtracting 8 from both sides gives:
\[
x = -8
\]
So, the response here is **-8**.
2. **For \( -6 + \_\_ = \text{negative number} \):**
The left-hand side of this equation must yield a negative number. We can rewrite it to find the conditions for this to be true:
\[
-6 + x < 0
\]
Adding 6 to each side results in:
\[
x < 6
\]
Thus, **any number less than 6** will satisfy this condition. Examples include **-7, -6, -5, 0, etc.**
3. **For \( \_\_ - (-8) = \text{positive number} \):**
We can simplify this to \( x + 8 \) since subtracting a negative is the same as adding a positive:
\[
x + 8 > 0
\]
Subtracting 8 from each side gives:
\[
x > -8
\]
Thus, **any number greater than -8** will satisfy this condition. Examples include **-7, 0, 1, 2, etc.**
To summarize:
- The answer for the first blank is **-8**.
- The second blank can be filled with any integer less than **6** (for example, **-7**).
- The third blank can be filled with any integer greater than **-8** (for example, **-7** as a valid response too).
If you need a clear specific response for each blank:
1. First box: **-8**
2. Second box: **-7** (or any number less than 6)
3. Third box: **-7** (or any number greater than -8)