Sure, let's go through each part of the question step-by-step.
### a) Compare the sum of [tex]\( (+7) \)[/tex] and [tex]\( (-9) \)[/tex] with the difference of [tex]\( (-9) \)[/tex] and [tex]\( (-12) \)[/tex].
First, calculate the sum of [tex]\( (+7) \)[/tex] and [tex]\( (-9) \)[/tex].
[tex]\[ (+7) + (-9) = 7 - 9 = -2 \][/tex]
Next, calculate the difference of [tex]\( (-9) \)[/tex] and [tex]\( (-12) \)[/tex].
[tex]\[ (-9) - (-12) = -9 + 12 = 3 \][/tex]
Now, compare the two results:
- Sum of [tex]\( (+7) \)[/tex] and [tex]\( (-9) \)[/tex] is [tex]\( -2 \)[/tex]
- Difference of [tex]\( (-9) \)[/tex] and [tex]\( (-12) \)[/tex] is [tex]\( 3 \)[/tex]
So they are not equal. The comparison is [tex]\( -2 \ne 3 \)[/tex].
### b) Write a mathematical expression to subtract the sum of [tex]\( (+7) \)[/tex] and [tex]\( (-9) \)[/tex] from [tex]\( (-12) \)[/tex].
First, write down the sum of [tex]\( (+7) \)[/tex] and [tex]\( (-9) \)[/tex]:
[tex]\[ (+7) + (-9) = -2 \][/tex]
Now, we need to subtract this sum from [tex]\( (-12) \)[/tex]:
[tex]\[ (-12) - \left[(+7) + (-9)\right] \][/tex]
### c) Simplify the expression and find the result.
Using the expression from part b:
[tex]\[ (-12) - \left[(+7) + (-9)\right] \][/tex]
We know from part a that [tex]\( (+7) + (-9) = -2 \)[/tex], so substitute [tex]\( -2 \)[/tex] into the expression:
[tex]\[ (-12) - (-2) = -12 + 2 = -10 \][/tex]
The result is [tex]\( -10 \)[/tex].
### d) (i) Is the result a whole number? Give reason.
Yes, the result [tex]\( -10 \)[/tex] is a whole number. A whole number is any of the numbers {0, 1, 2, 3, ...} and their negative counterparts, including zero. Since [tex]\( -10 \)[/tex] is an integer from the set of whole numbers, it qualifies as a whole number.
