Certainly! Let's review Akeem's work and solve the equation correctly.
### Part A: Review Akeem's Work
Firstly, let's review Akeem's steps to find where the mistake happened.
1. Step 1:
[tex]\[
\frac{d}{0.13} = 5.2
\][/tex]
This step is correct and sets up the initial equation correctly.
2. Step 2:
[tex]\[
0.13 \cdot \frac{d}{0.13} = \frac{5.2}{0.13}
\][/tex]
Akeem tried to clear the fraction by multiplying both sides by [tex]\(0.13\)[/tex]. However, there’s an error in performing the operation correctly. The left side should simplify to [tex]\(d\)[/tex], but it seems he might have incorrectly applied the multiplication to the right side as well.
3. Step 3:
[tex]\[
d = 40
\][/tex]
This result appears after the incorrect Step 2 and is therefore incorrect.
Error Identification:
- The mistake occurred in Step 2. The correct procedure involves multiplying both sides of the equation by [tex]\(0.13\)[/tex] to clear the denominator, not taking reciprocal operations, which leads to incorrect simplification. The correct simplification should be:
[tex]\[
\frac{d}{0.13} \cdot 0.13 = 5.2 \cdot 0.13
\][/tex]
### Part B: Correct Solution
Now, let's solve the equation step-by-step correctly.
1. Original Equation:
[tex]\[
\frac{d}{0.13} = 5.2
\][/tex]
2. Multiply both sides by [tex]\(0.13\)[/tex] to isolate [tex]\(d\)[/tex]:
[tex]\[
\left( \frac{d}{0.13} \right) \cdot 0.13 = 5.2 \cdot 0.13
\][/tex]
3. Simplify the left side:
[tex]\[
d = 5.2 \cdot 0.13
\][/tex]
4. Perform the multiplication:
[tex]\[
d = 0.676
\][/tex]
Thus, the correct value of [tex]\(d\)[/tex] is [tex]\(\boxed{0.676}\)[/tex].
