Let's carefully examine the steps Cara took to evaluate the expression [tex]\(\frac{4(7-13)}{3} + (-4)^2 - 2(6-2)\)[/tex].
### Cara's Steps:
1. Step 1:
[tex]\[
\frac{4(7-13)}{3} + (-4)^2 - 2(4)
\][/tex]
Cara simplified [tex]\(6-2\)[/tex] correctly to 4, but let's look closely at the step with [tex]\(7 - 13\)[/tex].
2. Step 2:
[tex]\[
\frac{28-13}{3} + (-4)^2 - 2(4)
\][/tex]
Here, Cara seems to have evaluated [tex]\(4(7-13)\)[/tex] incorrectly. She wrote [tex]\(28 - 13\)[/tex] instead of correctly evaluating the subtraction [tex]\(7 - 13\)[/tex], which leads to [tex]\(-6\)[/tex].
### Correct Steps:
Let's consider how the expression should have been evaluated correctly:
1. Step 1:
[tex]\[
7 - 13 = -6
\][/tex]
Therefore,
[tex]\[
4(7-13) = 4(-6) = -24
\][/tex]
The expression should be:
[tex]\[
\frac{-24}{3} + (-4)^2 - 2(6-2)
\][/tex]
2. Step 2:
[tex]\[
\frac{-24}{3} + 16 - 2(4)
\][/tex]
Dividing [tex]\(-24\)[/tex] by 3:
[tex]\[
\frac{-24}{3} = -8
\][/tex]
3. Step 3:
Calculation for:
[tex]\[
(-4)^2 = 16
\][/tex]
4. Step 4:
Calculation for:
[tex]\[
6 - 2 = 4 \quad \text{and} \quad 2(4) = 8
\][/tex]
5. Compiling Everything:
[tex]\[
-8 + 16 - 8 = 0
\][/tex]
From this walkthrough, the first error Cara made was in evaluating the subtraction [tex]\(7 - 13\)[/tex]. Instead of simplifying [tex]\(7 - 13\)[/tex] to [tex]\(-6\)[/tex], she erroneously seemed to have evaluated [tex]\(4(7-13)\)[/tex] as [tex]\(4(7) - 13 = 28 - 13\)[/tex].
### Conclusion:
Cara's first mistake was not evaluating [tex]\(7 - 13\)[/tex] correctly. Therefore, the correct answer is:
Cara did not evaluate [tex]\(7-13\)[/tex].
