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I'll now solve the six equations step by step:

### 1. \( \frac{1}{5}a + 1 = \frac{3}{10} \)
- Subtract 1 from both sides:
  \[
  \frac{1}{5}a = \frac{3}{10} - 1 = \frac{3}{10} - \frac{10}{10} = \frac{-7}{10}
  \]
- Multiply both sides by 5:
  \[
  a = 5 \times \frac{-7}{10} = \frac{-35}{10} = -3.5
  \]

### 2. \( \frac{n}{3} - \frac{1}{6} = \frac{1}{2} \)
- Add \( \frac{1}{6} \) to both sides:
  \[
  \frac{n}{3} = \frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}
  \]
- Multiply both sides by 3:
  \[
  n = 3 \times \frac{2}{3} = 2
  \]

### 3. \( \frac{5}{6}c + \frac{1}{2} = \frac{2}{3} \)
- Subtract \( \frac{1}{2} \) from both sides:
  \[
  \frac{5}{6}c = \frac{2}{3} - \frac{1}{2} = \frac{4}{6} - \frac{3}{6} = \frac{1}{6}
  \]
- Multiply both sides by \( \frac{6}{5} \):
  \[
  c = \frac{1}{6} \times \frac{6}{5} = \frac{6}{30} = \frac{1}{5}
  \]

### 4. \( \frac{k}{5} + \frac{3k}{10} = \frac{3}{2} \)
- Combine like terms: 
  \[
  \frac{2k}{10} + \frac{3k}{10} = \frac{5k}{10} = \frac{k}{2}
  \]
- Now solve \( \frac{k}{2} = \frac{3}{2} \):
  \[
  k = 3
  \]

### 5. \( \frac{2}{5}g + 2 = \frac{4}{7} \)
- Subtract 2 from both sides:
  \[
  \frac{2}{5}g = \frac{4}{7} - 2 = \frac{4}{7} - \frac{14}{7} = \frac{-10}{7}
  \]
- Multiply both sides by \( \frac{5}{2} \):
  \[
  g = \frac{-10}{7} \times \frac{5}{2} = \frac{-50}{14} = \frac{-25}{7}
  \]

### 6. \( \frac{h}{6} + \frac{2}{3} = \frac{5}{4} \)
- Subtract \( \frac{2}{3} \) from both sides:
  \[
  \frac{h}{6} = \frac{5}{4} - \frac{2}{3} = \frac{15}{12} - \frac{8}{12} = \frac{7}{12}
  \]
- Multiply both sides by 6:
  \[
  h = 6 \times \frac{7}{12} = \frac{42}{12} = 3.5
  \]

### Summary of Solutions:
1. \( a = -3.5 \)
2. \( n = 2 \)
3. \( c = \frac{1}{5} \)
4. \( k = 3 \)
5. \( g = \frac{-25}{7} \)
6. \( h = 3.5 \)

Would you like further details on any of these steps? Here are some follow-up questions:

1. How do you handle equations with fractions?
2. What is the process of finding a common denominator in subtraction?
3. How do you approach equations with multiple variables?
4. What are common errors to avoid when working with fractions?
5. How does multiplying by the reciprocal simplify equations?

**Tip:** Always simplify fractions before performing operations for cleaner calculations.

Learn how to solve linear equations involving fractions and mixed terms, including step-by-step explanations. This problem set covers core algebraic principles like working with fractions and simplifying terms, ideal for students in Grades 6-9.

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