Let's solve the equation:

\[
\frac{X}{4} - \left(\frac{2X - 3}{6}\right) = 3
\]

### Step 1: Eliminate the fractions
To eliminate the fractions, we need to find the least common denominator (LCD) of 4 and 6, which is 12. Multiply the entire equation by 12 to clear the denominators:

\[
12 \times \left(\frac{X}{4}\right) - 12 \times \left(\frac{2X - 3}{6}\right) = 12 \times 3
\]

Simplifying each term:

\[
3X - 2(2X - 3) = 36
\]

### Step 2: Distribute the -2
Now distribute the -2 over the terms inside the parentheses:

\[
3X - (4X - 6) = 36
\]

\[
3X - 4X + 6 = 36
\]

### Step 3: Combine like terms
Combine the \(3X\) and \(-4X\):

\[
-X + 6 = 36
\]

### Step 4: Solve for \(X\)
Subtract 6 from both sides:

\[
-X = 36 - 6
\]

\[
-X = 30
\]

Multiply both sides by -1:

\[
X = -30
\]

### Final answer:
\[
X = -30
\]

Would you like a more detailed explanation or further clarification?

### Related questions:
1. How do you solve linear equations with fractions?
2. What are common methods to simplify equations with multiple variables?
3. How can you check if your solution to an equation is correct?
4. What are the steps for distributing negative signs in equations?
5. How can you solve equations with variables on both sides?

**Tip:** Always double-check your work by plugging the solution back into the original equation.

Learn how to solve the linear equation X/4 – (2X – 3/6) = 3 with a detailed step-by-step solution. This problem covers key algebra concepts, including simplifying equations by eliminating fractions and applying the distributive property. Suitable for students in Grades 8-10.

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