Sure, let me provide a detailed step-by-step solution for each part of the question.
### Part a) [tex]\( |-2| + 4 \)[/tex]
1. Calculate the absolute value of [tex]\(-2\)[/tex]:
[tex]\[
|-2| = 2
\][/tex]
2. Add 4 to the result:
[tex]\[
2 + 4 = 6
\][/tex]
So, [tex]\( |-2| + 4 = 6 \)[/tex].
### Part b) [tex]\( |-5| + |-2| - 3 \)[/tex]
1. Calculate the absolute value of [tex]\(-5\)[/tex]:
[tex]\[
|-5| = 5
\][/tex]
2. Calculate the absolute value of [tex]\(-2\)[/tex]:
[tex]\[
|-2| = 2
\][/tex]
3. Add the results and then subtract 3:
[tex]\[
5 + 2 - 3 = 4
\][/tex]
So, [tex]\( |-5| + |-2| - 3 = 4 \)[/tex].
### Part c) [tex]\( 2 + |-3| - |-5| \)[/tex]
1. Calculate the absolute value of [tex]\(-3\)[/tex]:
[tex]\[
|-3| = 3
\][/tex]
2. Calculate the absolute value of [tex]\(-5\)[/tex]:
[tex]\[
|-5| = 5
\][/tex]
3. Add 2 to the absolute value of [tex]\(-3\)[/tex] and then subtract the absolute value of [tex]\(-5\)[/tex]:
[tex]\[
2 + 3 - 5 = 0
\][/tex]
So, [tex]\( 2 + |-3| - |-5| = 0 \)[/tex].
### Part d) [tex]\( |3 - |-5|| \)[/tex]
1. Calculate the absolute value of [tex]\(-5\)[/tex]:
[tex]\[
|-5| = 5
\][/tex]
2. Subtract this result from 3:
[tex]\[
3 - 5 = -2
\][/tex]
3. Finally, calculate the absolute value of the result:
[tex]\[
|-2| = 2
\][/tex]
So, [tex]\( |3 - |-5|| = 2 \)[/tex].
Therefore, the results are:
1. [tex]\( |-2| + 4 = 6 \)[/tex]
2. [tex]\( |-5| + |-2| - 3 = 4 \)[/tex]
3. [tex]\( 2 + |-3| - |-5| = 0 \)[/tex]
4. [tex]\( |3 - |-5|| = 2 \)[/tex]
