Question

What is the solution to the linear equation?

StartFraction 2 Over 5 EndFraction plus p equals StartFraction 4 Over 5 EndFraction plus StartFraction 3 Over 5 EndFraction p. + p = + p

p = 1
p = 2
p = 8
p = 10

Answer 1

To solve the linear equation

\[
\frac{2}{5} + p = \frac{4}{5} + \frac{3}{5}p,
\]

let's first isolate \( p \).

1. Start with the original equation:
\[
\frac{2}{5} + p = \frac{4}{5} + \frac{3}{5}p.
\]

2. Next, subtract \(\frac{3}{5}p\) from both sides:
\[
\frac{2}{5} + p - \frac{3}{5}p = \frac{4}{5}.
\]
This simplifies to:
\[
\frac{2}{5} + \left(1 - \frac{3}{5}\right)p = \frac{4}{5}
\]
or
\[
\frac{2}{5} + \frac{2}{5}p = \frac{4}{5}.
\]

3. Now, subtract \(\frac{2}{5}\) from both sides:
\[
\frac{2}{5}p = \frac{4}{5} - \frac{2}{5}.
\]
Simplifying the right side gives:
\[
\frac{2}{5}p = \frac{2}{5}.
\]

4. Finally, divide both sides by \(\frac{2}{5}\):
\[
p = 1.
\]

Therefore, the solution to the linear equation is

\[
\boxed{1}.
\]