Sure, let's analyze the expression [tex]\(8 + \frac{1}{2} \times (6 - 2) - 1\)[/tex] to understand which statement accurately describes it.
1. First, we need to evaluate the terms within the parentheses:
[tex]\[
6 - 2 = 4
\][/tex]
2. Next, we take half of this result:
[tex]\[
\frac{1}{2} \times 4 = 2
\][/tex]
3. Add this to 8:
[tex]\[
8 + 2 = 10
\][/tex]
4. Finally, we subtract 1:
[tex]\[
10 - 1 = 9
\][/tex]
Now, let’s find the description that matches this operation:
1. 8 more than half the difference of 2 and 1, and then subtract 6:
[tex]\[
8 + \frac{1}{2} \times (2 - 1) - 6
\][/tex]
Simplifying inside the parentheses:
[tex]\[
2 - 1 = 1
\][/tex]
Taking half:
[tex]\[
\frac{1}{2} \times 1 = 0.5
\][/tex]
Adding to 8:
[tex]\[
8 + 0.5 = 8.5
\][/tex]
Subtract 6:
[tex]\[
8.5 - 6 = 2.5
\][/tex]
This does not match our expression which evaluates to 9.
2. Add 8 to half the difference of 6 and 2, then subtract 1:
[tex]\[
8 + \frac{1}{2} \times (6 - 2) - 1
\][/tex]
Simplifying inside the parentheses:
[tex]\[
6 - 2 = 4
\][/tex]
Taking half:
[tex]\[
\frac{1}{2} \times 4 = 2
\][/tex]
Adding to 8:
[tex]\[
8 + 2 = 10
\][/tex]
Finally, subtract 1:
[tex]\[
10 - 1 = 9
\][/tex]
This matches our calculated expression.
3. The sum of 8 and [tex]\(\frac{1}{2}\)[/tex] times 6 plus 2 minus 1:
[tex]\[
8 + \frac{1}{2} \times 6 + 2 - 1
\][/tex]
First evaluate the part multiplication:
[tex]\[
\frac{1}{2} \times 6 = 3
\][/tex]
Then sum with 8:
[tex]\[
8 + 3 = 11
\][/tex]
Add 2:
[tex]\[
11 + 2 = 13
\][/tex]
Subtract 1:
[tex]\[
13 - 1 = 12
\][/tex]
This does not match our expression which evaluates to 9.
The correct statement is: Add 8 to half the difference of 6 and 2, then subtract 1.
So, the answer is Option 2.
