To solve the inequality:

\[
\frac{1}{3}x - \frac{1}{4}(2x - 5) < \frac{1}{5}
\]

1. Distribute \(-\frac{1}{4}\) over \((2x - 5)\):
   \[
   \frac{1}{3}x - \frac{1}{4} \cdot 2x + \frac{1}{4} \cdot 5 < \frac{1}{5}
   \]
   This simplifies to:
   \[
   \frac{1}{3}x - \frac{1}{2}x + \frac{5}{4} < \frac{1}{5}
   \]

2. Combine the terms with \(x\):
   \[
   \left(\frac{1}{3} - \frac{1}{2}\right)x + \frac{5}{4} < \frac{1}{5}
   \]

3. Find a common denominator to combine the fractions:
   \[
   \frac{2}{6} - \frac{3}{6} = -\frac{1}{6}
   \]
   So we have:
   \[
   -\frac{1}{6}x + \frac{5}{4} < \frac{1}{5}
   \]

4. Move \(\frac{5}{4}\) to the other side:
   \[
   -\frac{1}{6}x < \frac{1}{5} - \frac{5}{4}
   \]

5. Find a common denominator for \(\frac{1}{5}\) and \(\frac{5}{4}\) (which is 20):
   \[
   \frac{1}{5} = \frac{4}{20} \quad \text{and} \quad \frac{5}{4} = \frac{25}{20}
   \]
   Then:
   \[
   \frac{1}{5} - \frac{5}{4} = \frac{4}{20} - \frac{25}{20} = -\frac{21}{20}
   \]
   So:
   \[
   -\frac{1}{6}x < -\frac{21}{20}
   \]

6. Multiply both sides by \(-6\) (and reverse the inequality sign):
   \[
   x > \frac{126}{20} = \frac{63}{10}
   \]

Thus, the solution is:

\[
x > \frac{63}{10} \quad \text{or} \quad x > 6.3
\]

Would you like more details, or do you have any questions?

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**5 Related Questions:**
1. How do you solve inequalities with fractions?
2. What happens when you multiply or divide by a negative number in inequalities?
3. Can you show a step-by-step guide to find a common denominator?
4. How do you handle distributing fractions over expressions in inequalities?
5. How do you interpret the solution to an inequality graphically?

**Tip:** When working with inequalities, always reverse the inequality sign if you multiply or divide by a negative number.

Explore how to solve the inequality 1/3x - 1/4(2x - 5) < 1/5 through step-by-step distribution, combining terms, and managing fractions. This problem covers key algebraic concepts and provides a clear approach to solving inequalities, suitable for Grades 8-10.

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