To solve the equation:

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

we'll follow these steps:

1. **Eliminate the fractions by finding a common denominator.**  
   The common denominator for 7 and 14 is 14.

2. **Rewrite each term with the common denominator:**

\[
\frac{2}{7}x = \frac{4}{14}x, \quad \frac{1}{7} = \frac{2}{14}, \quad \text{and} \quad \frac{3}{14} = \frac{3}{14}.
\]

So the equation becomes:

\[
\frac{4}{14}x - \frac{2}{14} = \frac{3}{14}.
\]

3. **Multiply every term by 14** to eliminate the denominators:

\[
14 \cdot \left( \frac{4}{14}x - \frac{2}{14} \right) = 14 \cdot \frac{3}{14}.
\]

This simplifies to:

\[
4x - 2 = 3.
\]

4. **Solve for \(x\):**

   - Add 2 to both sides:

\[
4x = 5.
\]

   - Divide both sides by 4:

\[
x = \frac{5}{4}.
\]

5. **Simplify the solution:**

\[
x = 1.25.
\]

The solution to the equation is \(x = 1.25\).

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. Solve \(\frac{3}{5}x - \frac{2}{5} = \frac{7}{10}\).
2. Solve \(2x - \frac{3}{4} = \frac{5}{2}\).
3. Solve \(\frac{5}{8}x + \frac{1}{2} = 1\).
4. Solve \(\frac{1}{3}x - \frac{1}{6} = \frac{1}{2}\).
5. Solve \(\frac{2}{9}x + \frac{4}{9} = 1\).

**Tip:** To eliminate fractions in equations, multiply every term by the least common multiple of all denominators.

Learn how to solve the equation 2/7x - 1/7 = 3/14 with a detailed step-by-step solution. This problem involves fractions and equations, focusing on multiplication of fractions to eliminate denominators. Suitable for students in Grades 6-8.

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