Let's solve the equation:

\[
\frac{5}{7} + \frac{3x}{2} = \frac{7}{14}
\]

### Step 1: Simplify the fractions where possible.
The fraction \(\frac{7}{14}\) simplifies to \(\frac{1}{2}\). So, the equation becomes:

\[
\frac{5}{7} + \frac{3x}{2} = \frac{1}{2}
\]

### Step 2: Subtract \(\frac{5}{7}\) from both sides of the equation.
To isolate \(\frac{3x}{2}\), subtract \(\frac{5}{7}\) from both sides:

\[
\frac{3x}{2} = \frac{1}{2} - \frac{5}{7}
\]

### Step 3: Find a common denominator to subtract the fractions.
The least common denominator between 2 and 7 is 14. Convert both fractions:

\[
\frac{1}{2} = \frac{7}{14}, \quad \frac{5}{7} = \frac{10}{14}
\]

Now, subtract the fractions:

\[
\frac{7}{14} - \frac{10}{14} = \frac{-3}{14}
\]

So, the equation becomes:

\[
\frac{3x}{2} = \frac{-3}{14}
\]

### Step 4: Solve for \(x\).
To find \(x\), multiply both sides by the reciprocal of \(\frac{3}{2}\), which is \(\frac{2}{3}\):

\[
x = \frac{-3}{14} \times \frac{2}{3} = \frac{-6}{42} = \frac{-1}{7}
\]

### Final Answer:
The solution is:

\[
x = -\frac{1}{7}
\]

Would you like further details or have any questions about the solution?

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Here are 5 related questions you might find interesting:
1. How would you solve the equation if the right side were a different fraction?
2. What happens if you change the coefficient of \(x\) from 3 to another number?
3. How can you check your solution to ensure it's correct?
4. How does multiplying both sides of an equation by a reciprocal work?
5. What if you had variables in the denominator, how would that change the approach?

**Tip:** When solving equations involving fractions, it's often helpful to find a common denominator early in the process to simplify your work!

Learn how to solve the fraction equation 5/7 + 3x/2 = 7/14 step by step. This problem covers algebraic concepts such as fraction subtraction and solving linear equations. Suitable for students in Grades 6-8.

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