Let's go through the solution step by step and identify where the mistake was made.
1. Original Expression:
[tex]\[
-6 + 8(11 - 4) + 3^2
\][/tex]
2. Step 1:
Evaluate the expression inside the parentheses first:
[tex]\[
-6 + 8(7) + 3^2
\][/tex]
This step is correct because [tex]\(11 - 4 = 7\)[/tex].
3. Step 2:
Next, evaluate the exponentiation:
[tex]\[
-6 + 8(7) + 9
\][/tex]
This step is also correct because [tex]\(3^2 = 9\)[/tex].
4. Step 3:
At this point, the order of operations (PEMDAS/BODMAS) indicates that multiplication should be performed before addition and subtraction:
[tex]\[
-6 + 56 + 9
\][/tex]
However, the step shown is:
[tex]\[
2(7) + 9
\][/tex]
This is incorrect because it seems to incorrectly simplify [tex]\(-6 + 8\)[/tex] as [tex]\(2\)[/tex].
Since we have identified that Step 3 is where the mistake occurs, let's confirm it by continuing the correct calculations:
Continuing from:
[tex]\[
-6 + 56 + 9
\][/tex]
5. Perform the addition and subtraction from left to right:
[tex]\[
(-6 + 56) + 9 = 50 + 9 = 59
\][/tex]
So the correct answer to the expression should be [tex]\(59\)[/tex].
Thus, the step where the mistake was made is Step 3.
