Sure, let's solve each of the expressions step-by-step.
### Expression 1: [tex]\( 7 - [-5 + (2 - 9 + 13 - 25)] \)[/tex]
1. Start by evaluating the innermost parenthesis:
[tex]\[
2 - 9 = -7
\][/tex]
2. Next, continue the expression inside the brackets:
[tex]\[
-7 + 13 = 6
\][/tex]
3. Then, substitute back into the expression:
[tex]\[
6 - 25 = -19
\][/tex]
4. Moving on, handle the outer part:
[tex]\[
-5 + (-19) = -24
\][/tex]
5. Finally, subtract this result from 7:
[tex]\[
7 - (-24) = 7 + 24 = 31
\][/tex]
So, the first expression evaluates to [tex]\(31\)[/tex].
### Expression 2: [tex]\(\{31 + \{17 - (12 - 43) - 19\} + 21\}\)[/tex]
1. Start by evaluating the innermost parenthesis:
[tex]\[
12 - 43 = -31
\][/tex]
2. Continue with the next layer:
[tex]\[
17 - (-31) = 17 + 31 = 48
\][/tex]
3. Subtract 19:
[tex]\[
48 - 19 = 29
\][/tex]
4. Add this result to 31:
[tex]\[
31 + 29 = 60
\][/tex]
5. Finally, add 21:
[tex]\[
60 + 21 = 81
\][/tex]
So, the second expression evaluates to [tex]\(81\)[/tex].
### Expression 3: [tex]\(18 + (26 - [35 - (1 - 13)] + 14) + 67\)[/tex]
1. Start with the innermost parenthesis:
[tex]\[
1 - 13 = -12
\][/tex]
2. Substitute back into the expression:
[tex]\[
35 - (-12) = 35 + 12 = 47
\][/tex]
3. Continue:
[tex]\[
26 - 47 = -21
\][/tex]
4. Add 14:
[tex]\[
-21 + 14 = -7
\][/tex]
5. Finally, handle the outermost parts:
[tex]\[
18 + (-7) + 67 = 11 + 67 = 78
\][/tex]
So, the third expression evaluates to [tex]\(50\)[/tex].
### Expression 4: [tex]\(-1 + \{-1 + 1 - 1 - 11 - 1 + [1 - 1]\} + 1\)[/tex]
1. Start with the innermost bracket:
[tex]\[
1 - 1 = 0
\][/tex]
2. Substitute back into the expression:
[tex]\[
-1 + 1 - 1 - 11 - 1 + 0 = -13
\][/tex]
3. Add the remaining -1 and +1:
[tex]\[
-1 - 13 + 1 = -13
\][/tex]
So, the fourth expression evaluates to [tex]\(-13\)[/tex].
Therefore, the final answers are:
1. [tex]\(31\)[/tex]
2. [tex]\(81\)[/tex]
3. [tex]\(50\)[/tex]
4. [tex]\(-13\)[/tex]
