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We are given the equation:

\[
\frac{1}{10} + \frac{h}{6} = \frac{28}{30} = \frac{14}{15}
\]

We need to find the value of \( h \).

### Step 1: Work with the first part of the equation
Start by solving:
\[
\frac{1}{10} + \frac{h}{6} = \frac{28}{30}
\]

First, convert all fractions to have the same denominator. The least common denominator (LCD) of 10, 6, and 30 is 30. Rewrite the fractions with a denominator of 30:

\[
\frac{1}{10} = \frac{3}{30}, \quad \frac{h}{6} = \frac{5h}{30}, \quad \frac{28}{30} = \frac{28}{30}
\]

So, the equation becomes:
\[
\frac{3}{30} + \frac{5h}{30} = \frac{28}{30}
\]

Now, combine the terms on the left side:
\[
\frac{3 + 5h}{30} = \frac{28}{30}
\]

### Step 2: Eliminate the denominators
Since the denominators are the same, we can equate the numerators:
\[
3 + 5h = 28
\]

### Step 3: Solve for \( h \)
Subtract 3 from both sides:
\[
5h = 28 - 3
\]
\[
5h = 25
\]

Now, divide by 5:
\[
h = \frac{25}{5} = 5
\]

### Final Answer:
The value of \( h \) is \( \boxed{5} \).

---

Would you like further clarification on any step? Here are some related questions for practice:

1. Solve for \( h \) in the equation \( \frac{h}{4} + \frac{2}{5} = \frac{7}{10} \).
2. What is the least common denominator of 8, 12, and 24?
3. Simplify the expression \( \frac{2}{7} + \frac{3}{14} \).
4. Solve for \( h \): \( \frac{1}{5} + \frac{h}{8} = \frac{9}{10} \).
5. Convert the fraction \( \frac{5}{6} \) to an equivalent fraction with denominator 24.

**Tip:** When adding or subtracting fractions, always find the least common denominator to simplify calculations.

1/10 + h/6 = 28/30 = 14/15. What is the value of h?

This page provides a step-by-step solution to solving the linear equation 1/10 + h/6 = 28/30. Learn how to handle fractional equations, find a common denominator, and isolate the variable h. Ideal for students in Grades 6-8.

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