High School

We appreciate your visit to Line 1 tex quad frac 3 5 y 8 4 tex Line 2 tex frac 5 3 cdot frac 3 5 y 12 cdot frac. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Line 1: [tex]$\quad \frac{3}{5} y - 8 = 4$[/tex]
Line 2: [tex]$\frac{5}{3} \cdot \frac{3}{5} y = 12 \cdot \frac{5}{3}$[/tex]
Line 3:
[tex]$\begin{array}{l}
y = \frac{60}{3} \\
y = 20
\end{array}$[/tex]

Penny's solving work is shown here. Has she solved this equation correctly?

A. Yes, Penny's work is correct and 20 is the correct solution.
B. No, Penny is wrong. She should have multiplied both sides by [tex]$\frac{5}{3}$[/tex].

Answer :

Let's go through Penny's solution step-by-step to see if she solved the equation correctly:

1. Original Equation:
[tex]\[
\frac{3}{5}y - 8 = 4
\][/tex]
This is the equation Penny started with.

2. Step 1: Isolate the Term with [tex]\(y\)[/tex]:

To solve for [tex]\(y\)[/tex], first add 8 to both sides to move the constant term to the right side:
[tex]\[
\frac{3}{5}y - 8 + 8 = 4 + 8
\][/tex]
Simplifying this gives:
[tex]\[
\frac{3}{5}y = 12
\][/tex]

3. Step 2: Solve for [tex]\(y\)[/tex]:

Next, multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{5}\)[/tex], which is [tex]\(\frac{5}{3}\)[/tex]:
[tex]\[
\left(\frac{5}{3}\right) \cdot \frac{3}{5}y = 12 \cdot \frac{5}{3}
\][/tex]
This simplifies the left side to [tex]\(y\)[/tex] because [tex]\(\frac{5}{3} \times \frac{3}{5} = 1\)[/tex]:
[tex]\[
y = 12 \cdot \frac{5}{3}
\][/tex]

Now, calculate the right side:
[tex]\[
y = \frac{60}{3}
\][/tex]
Simplifying the division gives:
[tex]\[
y = 20
\][/tex]

4. Conclusion:

Yes, Penny correctly solved for [tex]\(y\)[/tex]. The solution [tex]\(y = 20\)[/tex] is indeed correct.

Thanks for taking the time to read Line 1 tex quad frac 3 5 y 8 4 tex Line 2 tex frac 5 3 cdot frac 3 5 y 12 cdot frac. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada