Let's solve the given expression step-by-step:
[tex]\[ 4 + \{[-7 + (3 + 2) - (-2)] + [(-3) - (+8 - 8) + (-10)]\} + 10 - 1 \][/tex]
1. Evaluate the innermost parentheses:
[tex]\[ 3 + 2 = 5 \][/tex]
2. Substitute this result back into the expression and simplify inside the brackets:
[tex]\[ [-7 + 5 - (-2)] \][/tex]
First, calculate [tex]\( -7 + 5 \)[/tex]:
[tex]\[ -7 + 5 = -2 \][/tex]
Next, subtract [tex]\(-2\)[/tex] which is the same as adding 2:
[tex]\[ -2 - (-2) = -2 + 2 = 0 \][/tex]
3. Now for the second bracket:
[tex]\[ (-3) - (+8 - 8) + (-10) \][/tex]
Calculate the intermediate step:
[tex]\[ +8 - 8 = 0 \][/tex]
Substitute this back into the expression:
[tex]\[ (-3) - 0 + (-10) \][/tex]
Simplify step-by-step:
[tex]\[ -3 - 0 = -3 \][/tex]
[tex]\[ -3 + (-10) = -3 - 10 = -13 \][/tex]
4. Combine the results from inside the curly brackets:
[tex]\[ \{[0] + [-13]\} \][/tex]
Simplify:
[tex]\[ 0 + (-13) = -13 \][/tex]
5. Substitute this result back into the original expression:
[tex]\[ 4 + (-13) + 10 - 1 \][/tex]
6. Finally, simplify the entire expression:
Calculate [tex]\( 4 + (-13) \)[/tex]:
[tex]\[ 4 - 13 = -9 \][/tex]
Next, add 10:
[tex]\[ -9 + 10 = 1 \][/tex]
Lastly, subtract 1:
[tex]\[ 1 - 1 = 0 \][/tex]
So, the step-by-step solution to the expression [tex]\( 4 + \{[-7 + (3 + 2) - (-2)] + [(-3) - (+8 - 8) + (-10)]\} + 10 - 1 \)[/tex] is:
[tex]\[ 4+\{[-7+(3+2)-(-2)]+[(-3)-(+8-8)+(-10)]\}+10-1 = 0 \][/tex]
