To determine the missing expression in Step 1, we need to follow the sequence of steps leading to the final evaluation of the given expression:
[tex]\[ [(-10 + 2) - 1] + (2 + 3) \][/tex]
### Detailed Step-by-Step Solution
1. Original Expression:
[tex]\[ [(-10 + 2) - 1] + (2 + 3) \][/tex]
2. Simplify inside the first set of brackets:
- First, evaluate the expression inside the innermost parentheses:
[tex]\[ (-10 + 2) = -8 \][/tex]
- Next, subtract 1 from the result:
[tex]\[ -8 - 1 = -9 \][/tex]
- So, the expression now simplifies to:
[tex]\[ [-9] + (2 + 3) \][/tex]
3. Simplify the second set of parentheses:
- Evaluate the expression inside the parentheses:
[tex]\[ 2 + 3 = 5 \][/tex]
- Thus, the expression now is:
[tex]\[ -9 + 5 \][/tex]
4. Combine and simplify:
- Finally, add the remaining terms:
[tex]\[ -9 + 5 = -4 \][/tex]
Let's match this step-by-step breakdown with the given steps:
- Step 2 provided in the problem is:
[tex]\[ -9 + 2 + 3 \][/tex]
So, based on this, the expression immediately before Step 2 must have been simplified to [tex]\( [-9] + (2 + 3) \)[/tex], which then transforms to [tex]${-9 + 2 + 3}$[/tex] in Step 2. However, Step 1 must include the necessary intermediate calculation:
The appropriate answer choice is the one that leads directly to simplifying the expressions inside the brackets:
- Given choices:
- [tex]\([ -10 + -1 + 2 ] + (2 + 3)\)[/tex]
- [tex]\([ -8 - 1 ] + (2 + 3)\)[/tex]
- [tex]\([ -10 + 1 ] + (2 + 3)\)[/tex]
Based on the evaluation from the initial expression:
- [tex]\((-10 + 2) - 1 = -8 - 1 = -9\)[/tex]
The correct Step 1 should reflect simplifying the first set of parentheses into [tex]\([ -8 - 1 ] + (2 + 3)\)[/tex]:
Thus, the missing expression in Step 1 is:
[tex]\[
[-8 - 1] + (2 + 3)
\][/tex]
Thus, the corresponding correct answer is:
[tex]\[
[-8 - 1] + (2 + 3)
\][/tex]
