Find detailed and accurate answers to your questions on IDNLearn.com. Discover comprehensive answers to your questions from our community of experienced professionals.

Mrs. Boyler wrote an equation on the board. She asked the students to solve for the variable, [tex]d[/tex]. Akeem solved it on his paper using the following steps.

\begin{tabular}{|l|l|}
\hline Step 1 & [tex]\frac{d}{0.13}=5.2[/tex] \\
\hline Step 2 & [tex](0.13) \frac{d}{0.13}=\frac{5.2}{(0.13)}[/tex] \\
\hline Step 3 & [tex]d=40[/tex] \\
\hline
\end{tabular}

Part A: Review Akeem's work for solving the equation. State the step in which the error occurred, and describe the error using your mathematical vocabulary. (2 points)

Part B: Solve the equation, correcting any errors you may find. Show all the steps in your work. (4 points)


Sagot :

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].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.