Sure, let's go through each problem step-by-step:
### 1. Find: [tex]\((-25) + (-18)\)[/tex]
When you add two negative numbers, you add their absolute values together and keep the negative sign.
[tex]\[
(-25) + (-18) = - (25 + 18) = -(43) = -43
\][/tex]
So, the result is [tex]\(-43\)[/tex].
### 2. Subtract [tex]\(-95\)[/tex] from [tex]\(0\)[/tex]
Subtracting a negative number is the same as adding its positive counterpart.
[tex]\[
0 - (-95) = 0 + 95 = 95
\][/tex]
So, the result is [tex]\(95\)[/tex].
### 3. Find the difference: [tex]\((-15) - (21)\)[/tex]
To find the difference between [tex]\(-15\)[/tex] and [tex]\(21\)[/tex], you subtract [tex]\(21\)[/tex] from [tex]\(-15\)[/tex]:
[tex]\[
(-15) - 21 = -15 - 21 = -36
\][/tex]
So, the result is [tex]\(-36\)[/tex].
### 4. Use the number line to find:
#### i) [tex]\(4 + (-6)\)[/tex]
Adding a negative number is equivalent to subtracting the positive value:
[tex]\[
4 + (-6) = 4 - 6 = -2
\][/tex]
So, the result is [tex]\(-2\)[/tex].
#### ii) [tex]\((-6) + (-3)\)[/tex]
Adding two negative numbers results in a negative number whose absolute value is the sum of the absolute values of the addends:
[tex]\[
(-6) + (-3) = - (6 + 3) = -9
\][/tex]
So, the result is [tex]\(-9\)[/tex].
### 5. The sum of two integers is [tex]\(-23\)[/tex]. If one of them is [tex]\(12\)[/tex], find the other.
Let [tex]\(x\)[/tex] be the other integer.
Given:
[tex]\[
12 + x = -23
\][/tex]
To find [tex]\(x\)[/tex]:
[tex]\[
x = -23 - 12 = -35
\][/tex]
So, the other integer is [tex]\(-35\)[/tex].
### 6. Write the following integers in ascending order: [tex]\(-9, -24, 26, -2, -11, 18, 9\)[/tex]
To arrange these integers in ascending order, we list them from the smallest to the largest:
[tex]\[
-24, -11, -9, -2, 9, 18, 26
\][/tex]
So, the sorted list is [tex]\([-24, -11, -9, -2, 9, 18, 26]\)[/tex].
