We are given the equation:

\[
\frac{7}{6} = w + \frac{2}{8}
\]

### Step-by-Step Solution:

1. First, simplify the fraction \(\frac{2}{8}\):
   \[
   \frac{2}{8} = \frac{1}{4}
   \]
   So, the equation becomes:
   \[
   \frac{7}{6} = w + \frac{1}{4}
   \]

2. Now, subtract \(\frac{1}{4}\) from both sides to isolate \(w\):
   \[
   \frac{7}{6} - \frac{1}{4} = w
   \]

3. To subtract these fractions, find a common denominator. The least common denominator (LCD) of 6 and 4 is 12.

   Convert \(\frac{7}{6}\) and \(\frac{1}{4}\) to have a denominator of 12:
   \[
   \frac{7}{6} = \frac{14}{12}, \quad \frac{1}{4} = \frac{3}{12}
   \]

4. Subtract the fractions:
   \[
   \frac{14}{12} - \frac{3}{12} = \frac{11}{12}
   \]

So, \(w = \frac{11}{12}\).

### Final Answer:
\[
w = \frac{11}{12}
\]

Would you like more details on any step or have further questions?

Here are 5 related questions to explore:

1. How do you subtract fractions with different denominators?
2. Can you explain how to simplify fractions?
3. What is the least common denominator (LCD), and how is it used in fraction operations?
4. How can we solve more complex linear equations with fractions?
5. What is the process to add or subtract mixed numbers?

**Tip:** When subtracting fractions, always look for the least common denominator (LCD) to make the calculation easier.

Learn how to solve the linear equation 7/6 = w + 2/8 step-by-step. This problem involves simplifying fractions, using the Least Common Denominator (LCD), and isolating the variable w. Suitable for students in Grades 6-8.

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