Let's solve the equation \( \frac{X}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4} \).

### Step 1: Eliminate the fractions
To eliminate the fractions, find the least common denominator (LCD) of the fractions involved. The denominators are 2, 5, 3, and 4. The LCD of 2, 5, 3, and 4 is 60.

### Step 2: Multiply the entire equation by the LCD
Multiply both sides of the equation by 60 to eliminate the fractions:

\[
60 \times \left(\frac{X}{2}\right) - 60 \times \left(\frac{1}{5}\right) = 60 \times \left(\frac{x}{3}\right) + 60 \times \left(\frac{1}{4}\right)
\]

This simplifies to:

\[
30X - 12 = 20x + 15
\]

### Step 3: Rearrange the equation
To get all the \(x\) terms on one side and the constants on the other side, subtract \(20x\) from both sides and add 12 to both sides:

\[
30X - 20x = 15 + 12
\]

\[
30X - 20x = 27
\]

### Step 4: Factor out the common term
Factor out \(x\) on the left side:

\[
10x = 27
\]

### Step 5: Solve for \(x\)
Divide both sides by 10:

\[
x = \frac{27}{10} = 2.7
\]

So, the solution is \(x = 2.7\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the least common denominator (LCD) of multiple fractions?
2. What are the methods to solve linear equations with fractions?
3. Can you solve an equation where variables appear on both sides?
4. What happens when you factor out common terms in an equation?
5. How can you check if the solution to an equation is correct?

**Tip:** When dealing with equations involving fractions, multiplying by the least common denominator is a powerful technique to simplify the problem quickly.

Learn how to solve the equation involving fractions: X/2 - 1/5 = x/3 + 1/4 with a step-by-step solution. This problem covers key concepts in equations, fractions, and variable isolation. Suitable for students in Grades 7-9.

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