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The three steps below were used to find the value of the expression

[tex]\[ [(-10 + 2) - 1] + (2 + 3) \][/tex]

Step 1: ?
Step 2: [tex]\(-9 + 2 + 3\)[/tex]
Step 3: [tex]\(-7 + 3\)[/tex]

Which expression is missing from Step 1?

A. [tex]\([(-10 + -1 + 2)] + (2 + 3)\)[/tex]
B. [tex]\([-8 - 1] + (2 + 3)\)[/tex]
C. [tex]\([(-10 + 1)] + (2 + 3)\)[/tex]

Sagot :

GinnyAnswer
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]
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