We are given the equation:

\[
\frac{1}{4}t + \frac{2}{5} = \frac{1}{5} - t
\]

### Step 1: Eliminate the fractions
We can eliminate the fractions by multiplying both sides of the equation by the least common denominator (LCD) of 4 and 5, which is 20. Multiply every term by 20:

\[
20 \times \left(\frac{1}{4}t + \frac{2}{5}\right) = 20 \times \left(\frac{1}{5} - t\right)
\]

This simplifies to:

\[
5t + 8 = 4 - 20t
\]

### Step 2: Move like terms to the same side
Add \(20t\) to both sides to move all terms involving \(t\) to the left side:

\[
5t + 20t + 8 = 4
\]

Simplifying:

\[
25t + 8 = 4
\]

### Step 3: Solve for \(t\)
Subtract 8 from both sides:

\[
25t = 4 - 8
\]

\[
25t = -4
\]

Now, divide by 25:

\[
t = \frac{-4}{25}
\]

### Final Answer:
\[
t = -\frac{4}{25}
\]

Would you like further explanation or details on any step?

Here are some related questions to explore:
1. How do you find the least common denominator (LCD) for fractions?
2. How can you handle equations with more variables?
3. What happens when both sides of an equation have fractions?
4. What is the process for solving linear equations?
5. How can you check your solution after solving an equation?

**Tip:** Always double-check your work by substituting your solution back into the original equation.

Explore how to solve the linear equation 1/4t + 2/5 = 1/5 - t, step by step, by eliminating fractions and isolating the variable. This guide focuses on algebraic concepts like finding the least common denominator and simplifying linear equations, suitable for students in Grades 7-8.

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