Garza Fleming
01/18/2024 · Primary School
\( \left. \begin{array} { l } { a = 5 , b = - 1 , c = 3 , d = - 2 } \\ { - a + ( - b ) - \{ - c - ( - d + a ) + [ - b + ( - b ) ] - d - [ - ( - a + b ) - c ] - d + ( - a ) \} } \end{array} \right. \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the expression given the values \( a = 5 \), \( b = -1 \), \( c = 3 \), and \( d = -2 \), we will substitute these values into the expression step by step.
The expression is:
\[
- a + ( - b ) - \{ - c - ( - d + a ) + [ - b + ( - b ) ] - d - [ - ( - a + b ) - c ] - d + ( - a ) \}
\]
Substituting the values:
1. \( a = 5 \)
2. \( b = -1 \)
3. \( c = 3 \)
4. \( d = -2 \)
Now, substituting these values into the expression:
\[
- 5 + ( - (-1) ) - \{ - 3 - ( - (-2) + 5 ) + [ - (-1) + ( - (-1) ) ] - (-2) - [ - ( - 5 + (-1) ) - 3 ] - (-2) + ( - 5 ) \}
\]
Now, simplify each part step by step:
1. Calculate \( - (-1) = 1 \):
\[
- 5 + 1 - \{ - 3 - ( 2 + 5 ) + [ 1 + 1 ] - (-2) - [ - ( - 5 - 1 ) - 3 ] - (-2) + ( - 5 ) \}
\]
2. Calculate \( 2 + 5 = 7 \):
\[
- 5 + 1 - \{ - 3 - 7 + [ 1 + 1 ] - (-2) - [ - ( - 6 ) - 3 ] - (-2) + ( - 5 ) \}
\]
3. Calculate \( [ 1 + 1 ] = 2 \):
\[
- 5 + 1 - \{ - 3 - 7 + 2 - (-2) - [ 6 - 3 ] - (-2) + ( - 5 ) \}
\]
4. Calculate \( - (-2) = 2 \):
\[
- 5 + 1 - \{ - 3 - 7 + 2 + 2 - [ 3 ] - (-2) + ( - 5 ) \}
\]
5. Now simplify \( - 3 - 7 + 2 + 2 = -6 \):
\[
- 5 + 1 - \{ - 6 - 3 + 2 + ( - 5 ) \}
\]
6. Combine \( - 6 - 3 = -9 \):
\[
- 5 + 1 - \{ - 9 + 2 + ( - 5 ) \}
\]
7. Combine \( - 9 + 2 = -7 \):
\[
- 5 + 1 - \{ - 7 - 5 \}
\]
8. Combine \( - 7 - 5 = -12 \):
\[
- 5 + 1 - (-12)
\]
9. This simplifies to:
\[
- 5 + 1 + 12
\]
10. Finally, calculate:
\[
- 5 + 1 = -4
\]
\[
-4 + 12 = 8
\]
Thus, the final result is:
\[
\boxed{8}
\]
Quick Answer
The final result is 8.
Answered by UpStudy AI and reviewed by a Professional Tutor
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