We are given the equation:

\[
\frac{X}{4} - 2X - \frac{3}{6} = 3
\]

Let's solve it step by step.

### Step 1: Simplify the constants
The term \(\frac{3}{6}\) simplifies to \(\frac{1}{2}\), so the equation becomes:

\[
\frac{X}{4} - 2X - \frac{1}{2} = 3
\]

### Step 2: Eliminate fractions
To eliminate the fractions, multiply the entire equation by 4 (the least common denominator of 4 and 2) to get rid of the denominators:

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

This gives us:

\[
X - 8X - 2 = 12
\]

### Step 3: Combine like terms
Now combine the \(X\) terms:

\[
X - 8X = -7X
\]

So the equation becomes:

\[
-7X - 2 = 12
\]

### Step 4: Isolate the variable term
Add 2 to both sides:

\[
-7X = 12 + 2
\]

\[
-7X = 14
\]

### Step 5: Solve for \(X\)
Finally, divide both sides by \(-7\):

\[
X = \frac{14}{-7}
\]

\[
X = -2
\]

So, the solution is:

\[
X = -2
\]

Do you have any questions or would you like more details on any step?

---

Here are 5 related questions to consider:
1. What happens if we multiply both sides of an equation by a negative number?
2. How would the solution change if we had a positive coefficient for \(X\)?
3. How do we deal with variables in the denominator in more complex equations?
4. What if the equation contained more terms with fractions?
5. How can we verify our solution is correct?

**Tip:** When solving equations with fractions, multiplying by the least common denominator (LCD) can quickly eliminate the fractions and simplify the problem!

Learn how to solve the linear equation X/4 – 2X – 3/6 = 3 with a detailed, step-by-step breakdown. This algebra problem involves simplifying fractions and solving for X. Suitable for students in Grades 8-10.

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