Let's analyze Carly's approach step-by-step to identify the first mistake in solving the equation [tex]\( 7a = 28 \)[/tex]:
1. Initial Equation:
[tex]\[
7a = 28
\][/tex]
This initial setup of the equation is correct.
2. Next Step (Setting Up):
[tex]\[
\frac{7a}{a} = \frac{28}{7}
\][/tex]
Here, Carly is attempting to simplify the equation. However, there is a mistake in this step. The error lies in dividing [tex]\(7a\)[/tex] by [tex]\(a\)[/tex]. The correct approach would be to divide both sides of the initial equation by 7, not by [tex]\(a\)[/tex]. Dividing by [tex]\(a\)[/tex] when [tex]\(a\)[/tex] could potentially be zero is not appropriate, and it does not simplify directly to the correct result.
The correct step should be:
[tex]\[
a = \frac{28}{7}
\][/tex]
When we simplify [tex]\(\frac{28}{7}\)[/tex], we get:
[tex]\[
a = 4
\][/tex]
3. Incorrect Result:
Carly's step:
[tex]\[
7 = 4
\][/tex]
is incorrect and it arises from the wrong simplification in the previous step.
The mistake Carly made was in step 2, during the setup process. She manipulated the equation incorrectly by choosing to divide by 'a' instead of 7.
So, the correct answer is:
(A) Setting up
