Sure, let's go through each of these step-by-step.
1. Subtracting [tex]\(+5\)[/tex] from [tex]\(-2\)[/tex]
When you subtract [tex]\(+5\)[/tex] from [tex]\(-2\)[/tex], you move 5 units to the left on the number line starting from [tex]\(-2\)[/tex]. From [tex]\(-2\)[/tex],
[tex]\[ -2 - 5 = -7 \][/tex]
Hence, the result is [tex]\(-7\)[/tex].
2. Adding [tex]\(-5\)[/tex] to [tex]\(+7\)[/tex]
When you add [tex]\(-5\)[/tex] to [tex]\(+7\)[/tex], you move 5 units to the left on the number line starting from [tex]\(+7\)[/tex]. From [tex]\(+7\)[/tex],
[tex]\[ 7 + (-5) = 2 \][/tex]
Hence, the result is [tex]\(2\)[/tex].
3. When [tex]\(-7\)[/tex] is subtracted from 0
When you subtract [tex]\(-7\)[/tex] from 0, it is equivalent to adding [tex]\(+7\)[/tex] to 0, since subtracting a negative number is addition. So,
[tex]\[ 0 - (-7) = 0 + 7 = 7 \][/tex]
Hence, the result is [tex]\(7\)[/tex].
4. To get [tex]\(+8\)[/tex], we have to subtract [tex]\(\_\_\_\_\)[/tex] from [tex]\(+12\)[/tex]
To find out what needs to be subtracted from [tex]\(+12\)[/tex] to get [tex]\(+8\)[/tex]:
[tex]\[ 12 - \text{?} = 8 \][/tex]
Solving for the unknown,
[tex]\[ \text{?} = 12 - 8 = 4 \][/tex]
So, we have to subtract [tex]\(4\)[/tex] from [tex]\(+12\)[/tex] to get [tex]\(+8\)[/tex].
5. Add [tex]\(\_\_\_\_\)[/tex] to [tex]\(-7\)[/tex] to get [tex]\(-4\)[/tex]
To find out what needs to be added to [tex]\(-7\)[/tex] to get [tex]\(-4\)[/tex]:
[tex]\[ -7 + \text{?} = -4 \][/tex]
Solving for the unknown,
[tex]\[ \text{?} = -4 - (-7) = -4 + 7 = 3 \][/tex]
So, we have to add [tex]\(3\)[/tex] to [tex]\(-7\)[/tex] to get [tex]\( -4\)[/tex].
