Sure, let's carefully examine the given expression step-by-step and identify where the error occurs, then we will find the correct result.
The given expression is:
[tex]\[ 2(4-16) - (-30) \][/tex]
### Step 1: Evaluate the Parentheses
First, solve the expression inside the parentheses:
[tex]\[ 4 - 16 = -12 \][/tex]
### Step 2: Perform the Multiplication
Next, multiply 2 by the result from the parentheses:
[tex]\[ 2 \times (-12) = -24 \][/tex]
### Step 3: Handle the Subtraction Involving a Negative Number
We need to subtract [tex]\(-30\)[/tex] from [tex]\(-24\)[/tex]. Subtracting a negative number is equivalent to adding its positive value:
[tex]\[ -24 - (-30) = -24 + 30 = 6 \][/tex]
So, the correct result is:
[tex]\[ 6 \][/tex]
### Examination of the Error
If we look at the intermediate steps provided:
[tex]\[
2(4-16) - (-30) \\
2(-12) - (-30) \\
24 - (-30) \quad \text{(This should be } -24 \text{ instead of } 24) \\
54 \quad \text{(This incorrectly adds } 30 \text{ to } 24)
\][/tex]
The error occurs in the third step:
[tex]\[ 2(-12) = -24 \][/tex]
This was incorrectly listed as [tex]\(24\)[/tex].
Thus, the correct final result of the given expression is:
[tex]\[ 6 \][/tex]
