you have to add 1 over 7 on both sides remember that so you add 3 over 14 with 1 over 7 and bring it down with 2 over 7 and the variable

To solve this problem, let's go through the steps using fractions as described:

1. **Add \( \frac{1}{7} \) to both sides:**

   This implies we are looking at an equation where we need to add \( \frac{1}{7} \) to both sides to maintain equality. Let's assume the equation on the left side involves adding fractions \( \frac{3}{14} \) and \( \frac{1}{7} \).

2. **Adding \( \frac{3}{14} \) and \( \frac{1}{7} \):**

   To add these fractions, they need a common denominator. The denominators are 14 and 7. The least common multiple of 14 and 7 is 14.

   - Convert \( \frac{1}{7} \) to a fraction with a denominator of 14:
     \[
     \frac{1}{7} = \frac{1 \times 2}{7 \times 2} = \frac{2}{14}
     \]

   - Now add \( \frac{3}{14} \) and \( \frac{2}{14} \):
     \[
     \frac{3}{14} + \frac{2}{14} = \frac{5}{14}
     \]

3. **Bringing down \( \frac{2}{7} \) and the variable:**

   Now, suppose the right-hand side of the equation involves \( \frac{2}{7} \) and a variable (let's call it \( x \)).

   To work with \( \frac{2}{7} \) and relate it to \( \frac{5}{14} \), let's express \( \frac{2}{7} \) with a denominator of 14:

   \[
   \frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}
   \]

4. **Combine both sides of the equation:**

   If we now combine the fractions and involve the variable, let's assume our goal is to equate something like \( \frac{5}{14} + x = \frac{4}{14} + x \). But typically, we have an expression on one side set equal to another expression. 

   If we consider these fractions involving \( x \):

   \[
   \frac{5}{14} + x = \frac{4}{14} + x
   \]

   Since both sides are equal, \( x \) must be such that this equality holds.

However, if we involve an unknown \( x \), or if there's an additional piece of information, we could manipulate this expression accordingly.

If there's a variable \( x \) to be isolated or another operation involving \( \frac{5}{14} \), it would depend on the full form of the equation. For now, assuming \( x \) is not yet defined, this is the process to deal with fractions on both sides.

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### Do you have any further details about the equation or additional terms involving \( x \) or other numbers?

### Additional Questions:
1. What are the complete terms of the original equation involving the variable \( x \)?
2. Would you like to know how to solve equations involving fractions and variables?
3. How would you handle an equation where \( x \) is on both sides of the equation?
4. Are there any other fraction operations you are curious about?
5. Do you need more examples of adding and simplifying fractions?

**Tip:** When working with fractions, always find a common denominator before adding or subtracting them to make the process easier!

Learn how to solve equations involving fractions by adding 1/7 on both sides. This detailed guide covers the step-by-step process using common denominators and variable isolation. Suitable for Grades 6-8.

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