To solve the equation \( x + \frac{3}{4} = 2x - \frac{1}{7} \), follow these steps:

1. **Subtract \( x \) from both sides** to get all terms involving \( x \) on one side:
   \[
   \frac{3}{4} = x - \frac{1}{7}
   \]

2. **Add \( \frac{1}{7} \) to both sides** to isolate \( x \):
   \[
   \frac{3}{4} + \frac{1}{7} = x
   \]

3. **Find a common denominator** to add the fractions on the left side. The least common denominator (LCD) of 4 and 7 is 28:
   \[
   \frac{3}{4} = \frac{21}{28}, \quad \frac{1}{7} = \frac{4}{28}
   \]
   Now add these fractions:
   \[
   \frac{21}{28} + \frac{4}{28} = \frac{25}{28}
   \]

4. Therefore, \( x = \frac{25}{28} \).

The solution is:
\[
x = \frac{25}{28}
\]

Would you like further details or have any questions?

Here are 8 related questions to expand on this topic:

1. How do you convert mixed fractions to improper fractions?
2. Can you explain how to find the least common denominator?
3. What steps are involved in solving a system of linear equations?
4. How do you check if your solution to a linear equation is correct?
5. What is the importance of isolating the variable in solving equations?
6. How do you add and subtract fractions with different denominators?
7. What is the process to simplify a fraction?
8. How do you solve equations with fractions on both sides?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the equation x + 3/4 = 2x - 1/7 step-by-step with detailed explanations and examples. This problem involves solving linear equations with fractions, isolating variables, and finding common denominators. Suitable for high school students in Grades 9-12.

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