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Sagot :
Let's go through each part of the problem step by step.
### Part (a)
[tex]\[ (25 - 8) - (-5 + 17) \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ 25 - 8 = 17 \][/tex]
[tex]\[ -5 + 17 = 12 \][/tex]
Now, combine the results:
[tex]\[ 17 - 12 = 5 \][/tex]
So, the answer for part (a) is [tex]\( 5 \)[/tex].
---
### Part (b)
[tex]\[ -13 - (-12 + 6) + (-19 + 8) \][/tex]
Handle the operations inside the parentheses first:
[tex]\[ -12 + 6 = -6 \][/tex]
[tex]\[ -19 + 8 = -11 \][/tex]
Now substitute back into the expression and combine the results in sequence:
[tex]\[ -13 - (-6) + (-11) \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ -13 + 6 - 11 \][/tex]
Now, perform the arithmetic:
[tex]\[ -13 + 6 = -7 \][/tex]
[tex]\[ -7 - 11 = -18 \][/tex]
So, the answer for part (b) is [tex]\( -18 \)[/tex].
---
### Part (c)
[tex]\[ -30 + (-25 + 18) - (-8 + 21) \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ -25 + 18 = -7 \][/tex]
[tex]\[ -8 + 21 = 13 \][/tex]
Substitute back into the expression:
[tex]\[ -30 + (-7) - 13 \][/tex]
Now, combine these results in sequence:
[tex]\[ -30 - 7 = -37 \][/tex]
[tex]\[ -37 - 13 = -50 \][/tex]
So, the answer for part (c) is [tex]\( -50 \)[/tex].
---
### Part (d)
[tex]\[ -24 - (1 - 7 + 4) \][/tex]
Handle the operations inside the parentheses:
[tex]\[ 1 - 7 = -6 \][/tex]
[tex]\[ -6 + 4 = -2 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ -24 - (-2) \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ -24 + 2 = -22 \][/tex]
So, the answer for part (d) is [tex]\( -22 \)[/tex].
---
### Part (e)
[tex]\[ 45 + (-15 - 5) + 4 \][/tex]
First, handle the operation inside the parentheses:
[tex]\[ -15 - 5 = -20 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ 45 + (-20) + 4 \][/tex]
Perform the arithmetic:
[tex]\[ 45 - 20 = 25 \][/tex]
[tex]\[ 25 + 4 = 29 \][/tex]
So, the answer for part (e) is [tex]\( 29 \)[/tex].
---
### Part (f)
[tex]\[ -(-20 - 31) - 6 + (2 - 15) \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ -20 - 31 = -51 \][/tex]
[tex]\[ 2 - 15 = -13 \][/tex]
Now substitute back into the expression:
[tex]\[ -(-51) - 6 + (-13) \][/tex]
Recall that subtracting a negative number is the same as adding its positive:
[tex]\[ 51 - 6 - 13 \][/tex]
Perform the arithmetic in sequence:
[tex]\[ 51 - 6 = 45 \][/tex]
[tex]\[ 45 - 13 = 32 \][/tex]
So, the answer for part (f) is [tex]\( 32 \)[/tex].
---
### Part (g)
[tex]\[ (-22 + 12) - (8 - 14) + 2 \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ -22 + 12 = -10 \][/tex]
[tex]\[ 8 - 14 = -6 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ -10 - (-6) + 2 \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ -10 + 6 + 2 \][/tex]
Perform the arithmetic in sequence:
[tex]\[ -10 + 6 = -4 \][/tex]
[tex]\[ -4 + 2 = -2 \][/tex]
So, the answer for part (g) is [tex]\( -2 \)[/tex].
---
### Part (h)
[tex]\[ -(5 - 9) + 2 + (3 - 7) + 9 \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ 5 - 9 = -4 \][/tex]
[tex]\[ 3 - 7 = -4 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ -(-4) + 2 + (-4) + 9 \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ 4 + 2 - 4 + 9 \][/tex]
Perform the arithmetic in sequence:
[tex]\[ 4 + 2 = 6 \][/tex]
[tex]\[ 6 - 4 = 2 \][/tex]
[tex]\[ 2 + 9 = 11 \][/tex]
So, the answer for part (h) is [tex]\( 11 \)[/tex].
---
In summary, the answers to the given operations are:
- Part (a): [tex]\( 5 \)[/tex]
- Part (b): [tex]\( -18 \)[/tex]
- Part (c): [tex]\( -50 \)[/tex]
- Part (d): [tex]\( -22 \)[/tex]
- Part (e): [tex]\( 29 \)[/tex]
- Part (f): [tex]\( 32 \)[/tex]
- Part (g): [tex]\( -2 \)[/tex]
- Part (h): [tex]\( 11 \)[/tex]
### Part (a)
[tex]\[ (25 - 8) - (-5 + 17) \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ 25 - 8 = 17 \][/tex]
[tex]\[ -5 + 17 = 12 \][/tex]
Now, combine the results:
[tex]\[ 17 - 12 = 5 \][/tex]
So, the answer for part (a) is [tex]\( 5 \)[/tex].
---
### Part (b)
[tex]\[ -13 - (-12 + 6) + (-19 + 8) \][/tex]
Handle the operations inside the parentheses first:
[tex]\[ -12 + 6 = -6 \][/tex]
[tex]\[ -19 + 8 = -11 \][/tex]
Now substitute back into the expression and combine the results in sequence:
[tex]\[ -13 - (-6) + (-11) \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ -13 + 6 - 11 \][/tex]
Now, perform the arithmetic:
[tex]\[ -13 + 6 = -7 \][/tex]
[tex]\[ -7 - 11 = -18 \][/tex]
So, the answer for part (b) is [tex]\( -18 \)[/tex].
---
### Part (c)
[tex]\[ -30 + (-25 + 18) - (-8 + 21) \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ -25 + 18 = -7 \][/tex]
[tex]\[ -8 + 21 = 13 \][/tex]
Substitute back into the expression:
[tex]\[ -30 + (-7) - 13 \][/tex]
Now, combine these results in sequence:
[tex]\[ -30 - 7 = -37 \][/tex]
[tex]\[ -37 - 13 = -50 \][/tex]
So, the answer for part (c) is [tex]\( -50 \)[/tex].
---
### Part (d)
[tex]\[ -24 - (1 - 7 + 4) \][/tex]
Handle the operations inside the parentheses:
[tex]\[ 1 - 7 = -6 \][/tex]
[tex]\[ -6 + 4 = -2 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ -24 - (-2) \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ -24 + 2 = -22 \][/tex]
So, the answer for part (d) is [tex]\( -22 \)[/tex].
---
### Part (e)
[tex]\[ 45 + (-15 - 5) + 4 \][/tex]
First, handle the operation inside the parentheses:
[tex]\[ -15 - 5 = -20 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ 45 + (-20) + 4 \][/tex]
Perform the arithmetic:
[tex]\[ 45 - 20 = 25 \][/tex]
[tex]\[ 25 + 4 = 29 \][/tex]
So, the answer for part (e) is [tex]\( 29 \)[/tex].
---
### Part (f)
[tex]\[ -(-20 - 31) - 6 + (2 - 15) \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ -20 - 31 = -51 \][/tex]
[tex]\[ 2 - 15 = -13 \][/tex]
Now substitute back into the expression:
[tex]\[ -(-51) - 6 + (-13) \][/tex]
Recall that subtracting a negative number is the same as adding its positive:
[tex]\[ 51 - 6 - 13 \][/tex]
Perform the arithmetic in sequence:
[tex]\[ 51 - 6 = 45 \][/tex]
[tex]\[ 45 - 13 = 32 \][/tex]
So, the answer for part (f) is [tex]\( 32 \)[/tex].
---
### Part (g)
[tex]\[ (-22 + 12) - (8 - 14) + 2 \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ -22 + 12 = -10 \][/tex]
[tex]\[ 8 - 14 = -6 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ -10 - (-6) + 2 \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ -10 + 6 + 2 \][/tex]
Perform the arithmetic in sequence:
[tex]\[ -10 + 6 = -4 \][/tex]
[tex]\[ -4 + 2 = -2 \][/tex]
So, the answer for part (g) is [tex]\( -2 \)[/tex].
---
### Part (h)
[tex]\[ -(5 - 9) + 2 + (3 - 7) + 9 \][/tex]
First, handle the operations inside the parentheses:
[tex]\[ 5 - 9 = -4 \][/tex]
[tex]\[ 3 - 7 = -4 \][/tex]
Now substitute back into the expression and combine the results:
[tex]\[ -(-4) + 2 + (-4) + 9 \][/tex]
Recall that subtracting a negative is the same as adding its positive:
[tex]\[ 4 + 2 - 4 + 9 \][/tex]
Perform the arithmetic in sequence:
[tex]\[ 4 + 2 = 6 \][/tex]
[tex]\[ 6 - 4 = 2 \][/tex]
[tex]\[ 2 + 9 = 11 \][/tex]
So, the answer for part (h) is [tex]\( 11 \)[/tex].
---
In summary, the answers to the given operations are:
- Part (a): [tex]\( 5 \)[/tex]
- Part (b): [tex]\( -18 \)[/tex]
- Part (c): [tex]\( -50 \)[/tex]
- Part (d): [tex]\( -22 \)[/tex]
- Part (e): [tex]\( 29 \)[/tex]
- Part (f): [tex]\( 32 \)[/tex]
- Part (g): [tex]\( -2 \)[/tex]
- Part (h): [tex]\( 11 \)[/tex]
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