We are given the equation:

\[
X + \frac{3}{7} = -X + \frac{1}{3} + \frac{4}{7}
\]

### Step 1: Combine like terms
First, let's move all the \( X \)-terms to one side and the constants to the other side. Add \( X \) to both sides:

\[
X + X + \frac{3}{7} = \frac{1}{3} + \frac{4}{7}
\]

This simplifies to:

\[
2X + \frac{3}{7} = \frac{1}{3} + \frac{4}{7}
\]

### Step 2: Simplify the constants
On the right-hand side, we need to combine the fractions \( \frac{1}{3} \) and \( \frac{4}{7} \). The least common denominator (LCD) of 3 and 7 is 21, so we convert both fractions:

\[
\frac{1}{3} = \frac{7}{21}, \quad \frac{4}{7} = \frac{12}{21}
\]

Now add the fractions:

\[
\frac{7}{21} + \frac{12}{21} = \frac{19}{21}
\]

So the equation becomes:

\[
2X + \frac{3}{7} = \frac{19}{21}
\]

### Step 3: Eliminate the fraction on the left-hand side
Now subtract \( \frac{3}{7} \) from both sides. We first convert \( \frac{3}{7} \) to have a denominator of 21:

\[
\frac{3}{7} = \frac{9}{21}
\]

So, we subtract:

\[
\frac{19}{21} - \frac{9}{21} = \frac{10}{21}
\]

Now the equation becomes:

\[
2X = \frac{10}{21}
\]

### Step 4: Solve for \( X \)
Finally, divide both sides by 2:

\[
X = \frac{10}{21} \times \frac{1}{2} = \frac{10}{42} = \frac{5}{21}
\]

Thus, the solution is:

\[
X = \frac{5}{21}
\]

Would you like further details or clarifications? 

Here are 5 related questions:
1. How do you add and subtract fractions with different denominators?
2. Can you solve \( X - \frac{1}{5} = 2X + \frac{4}{7} \)?
3. How do you multiply fractions by whole numbers?
4. What is the process for solving linear equations with fractions on both sides?
5. Can you convert improper fractions to mixed numbers?

**Tip**: When dealing with equations containing fractions, it's often helpful to find a common denominator early to simplify your work.

Learn how to solve the linear equation X + 3/7 = -X + 1/3 + 4/7 with a step-by-step guide. The solution explains the process of combining like terms and working with fractions, making it suitable for students in Grades 6-8.

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