To solve the equation:

\[
\frac{2}{7}(4x - 1) = \frac{3}{4}(1 - 5x)
\]

we will first eliminate the fractions by finding a common multiple of the denominators (7 and 4) and multiplying both sides by it. The least common multiple of 7 and 4 is 28.

### Step-by-Step Solution:

1. **Multiply both sides by 28:**

\[
28 \cdot \left( \frac{2}{7} (4x - 1) \right) = 28 \cdot \left( \frac{3}{4} (1 - 5x) \right)
\]

This simplifies to:

\[
8(4x - 1) = 21(1 - 5x)
\]

2. **Expand both sides:**

\[
32x - 8 = 21 - 105x
\]

3. **Combine like terms by adding \(105x\) to both sides:**

\[
32x + 105x - 8 = 21
\]

\[
137x - 8 = 21
\]

4. **Add 8 to both sides:**

\[
137x = 29
\]

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

\[
x = \frac{29}{137}
\]

### Solution:

\[
x = \frac{29}{137}
\]

Would you like a more detailed explanation of any step? 

Here are 5 related questions you might find interesting:

1. How do you solve equations involving fractions with different denominators?
2. What are the steps to solve linear equations with variables on both sides?
3. How can you verify the solution of an equation?
4. What is the importance of finding the least common multiple in equations involving fractions?
5. How do you solve equations with fractions without finding the least common multiple?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation to ensure both sides are equal.

Explore how to solve the linear equation 2/7(4x-1) = 3/4(1-5x) with a detailed, step-by-step explanation. Learn about multiplying both sides, using the distributive property, and balancing variables. Ideal for students in Grades 8-10.

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