Sure, let’s go through the detailed step-by-step solutions for each part.
### Part (b)
Evaluate the expression:
[tex]\[ 13 + 36 + (-4) + 2 - 16 + 4 - 25 + 10 + 24 + (-4 - 2) \][/tex]
1. Combine the constants directly:
[tex]\[ = 13 + 36 - 4 + 2 - 16 + 4 - 25 + 10 + 24 - 4 - 2 \][/tex]
2. Perform the addition and subtraction step-by-step:
[tex]\[ = (13 + 36) = 49 \][/tex]
[tex]\[ 49 - 4 = 45 \][/tex]
[tex]\[ 45 + 2 = 47 \][/tex]
[tex]\[ 47 - 16 = 31 \][/tex]
[tex]\[ 31 + 4 = 35 \][/tex]
[tex]\[ 35 - 25 = 10 \][/tex]
[tex]\[ 10 + 10 = 20 \][/tex]
[tex]\[ 20 + 24 = 44 \][/tex]
[tex]\[ 44 - 4 = 40 \][/tex]
[tex]\[ 40 - 2 = 38 \][/tex]
Therefore, the result for part (b) is:
[tex]\[ 38 \][/tex]
### Part (c)
Evaluate the expression:
[tex]\[ 12 + 3 - 15 + (-2 - 1) + 30 - 64 + 8 - 2 + 10 - 72 + (-8) \][/tex]
1. Combine the constants directly:
[tex]\[ = 12 + 3 - 15 - 2 - 1 + 30 - 64 + 8 - 2 + 10 - 72 - 8 \][/tex]
2. Perform the addition and subtraction step-by-step:
[tex]\[ = (12 + 3) = 15 \][/tex]
[tex]\[ 15 - 15 = 0 \][/tex]
[tex]\[ 0 - 2 = -2 \][/tex]
[tex]\[ -2 - 1 = -3 \][/tex]
[tex]\[ -3 + 30 = 27 \][/tex]
[tex]\[ 27 - 64 = -37 \][/tex]
[tex]\[ -37 + 8 = -29 \][/tex]
[tex]\[ -29 - 2 = -31 \][/tex]
[tex]\[ -31 + 10 = -21 \][/tex]
[tex]\[ -21 - 72 = -93 \][/tex]
[tex]\[ -93 - 8 = -101 \][/tex]
Therefore, the result for part (c) is:
[tex]\[ -101 \][/tex]
### Evaluating Final Expression
Evaluate the expression:
[tex]\[ (5 - 3) \times \left[(-6) + (5 + 7) - (-5)\right] - \left[(5 + 6) - (-7 + 9) + (-2)\right] \][/tex]
1. Simplify inside the brackets first:
Inside the first set of brackets:
[tex]\[ 5 - 3 = 2 \][/tex]
[tex]\[ (5 + 7) = 12 \][/tex]
[tex]\[ (-6) + 12 - (-5) \][/tex]
Note that subtracting a negative is the same as adding a positive:
[tex]\[ -6 + 12 + 5 = 11 \][/tex]
The expression then looks like:
[tex]\[ 2 \times 11 \][/tex]
Inside the second set of brackets:
[tex]\[ (5 + 6) - (-7 + 9) + (-2) \][/tex]
[tex]\[ 5 + 6 = 11 \][/tex]
[tex]\[ -7 + 9 = 2 \][/tex]
[tex]\[ 11 - 2 - 2 \][/tex]
[tex]\[ 11 - 2 = 9 - 2 \][/tex]
[tex]\[ = 7 \][/tex]
So, the whole expression becomes:
[tex]\[ 2 \times 11 - 7 = 22 - 7 = 15 \][/tex]
Therefore, the result for the final expression is:
[tex]\[ 15 \][/tex]
### Final Results:
- Part (b): [tex]\( 38 \)[/tex]
- Part (c): [tex]\( -101 \)[/tex]
- Final Expression: [tex]\( 15 \)[/tex]
