Let's solve the given expressions step by step.
First Expression: \( -58 - 3 + 2 + [7 - 2(5 - 3)] \)
1. First, we solve the innermost parentheses \( (5 - 3) \).
[tex]\[
5 - 3 = 2
\][/tex]
2. Next, we multiply the result by 2.
[tex]\[
2 \times 2 = 4
\][/tex]
3. We then subtract this result from 7.
[tex]\[
7 - 4 = 3
\][/tex]
4. Now, we substitute this result back into the original expression:
[tex]\[
-58 - 3 + 2 + 3
\][/tex]
5. Finally, we perform the addition and subtraction from left to right:
[tex]\[
-58 - 3 = -61
\][/tex]
[tex]\[
-61 + 2 = -59
\][/tex]
[tex]\[
-59 + 3 = -56
\][/tex]
So, the result for the first expression is \(-56\).
Second Expression: \( -5\{-3 + 2 + [7 - 2 + (2)]\} \)
1. First, we solve the innermost parentheses \( (2) \). This value is already 2.
2. Next, we simplify within the square brackets \( 7 - 2 + 2 \).
[tex]\[
7 - 2 = 5
\][/tex]
[tex]\[
5 + 2 = 7
\][/tex]
3. We substitute this result back into the expression inside the curly braces:
[tex]\[
-3 + 2 + 7
\][/tex]
4. Now, we perform the addition and subtraction from left to right:
[tex]\[
-3 + 2 = -1
\][/tex]
[tex]\[
-1 + 7 = 6
\][/tex]
5. Finally, we multiply this result by \(-5\):
[tex]\[
-5 \times 6 = -30
\][/tex]
So, the result for the second expression is [tex]\(-30\)[/tex].
