https://file.aiquickdraw.com/mathbot/file/1725972376902w688agz6.jpg

The equation given in the image is:

\[
\frac{x}{3} - \frac{5}{6} = \frac{3(x - 3)}{12}
\]

Let's solve for \(x\) step by step.

### Step 1: Simplify the right-hand side.
We can simplify the fraction on the right-hand side:

\[
\frac{3(x - 3)}{12} = \frac{x - 3}{4}
\]

So the equation becomes:

\[
\frac{x}{3} - \frac{5}{6} = \frac{x - 3}{4}
\]

### Step 2: Eliminate the fractions by finding a common denominator.
The common denominator for 3, 6, and 4 is 12. Let's multiply both sides of the equation by 12 to eliminate the fractions:

\[
12 \left( \frac{x}{3} \right) - 12 \left( \frac{5}{6} \right) = 12 \left( \frac{x - 3}{4} \right)
\]

This simplifies to:

\[
4x - 10 = 3(x - 3)
\]

### Step 3: Distribute and solve for \(x\).
Distribute the 3 on the right-hand side:

\[
4x - 10 = 3x - 9
\]

Now, subtract \(3x\) from both sides:

\[
x - 10 = -9
\]

Add 10 to both sides:

\[
x = 1
\]

### Final Answer:
The solution is \(x = 1\), which corresponds to option **B** in the multiple-choice options.

Would you like more details or have any questions?

Here are some related questions for deeper understanding:

1. How do you solve equations with variables on both sides?
2. How do you find the least common denominator of fractions?
3. What steps are involved in clearing fractions in an equation?
4. Can you explain how to distribute a number over parentheses?
5. What happens if the equation has no solutions or infinite solutions?

**Tip:** When solving equations with fractions, multiplying both sides by the least common denominator helps eliminate the fractions and simplifies the equation.

Step-by-step solution to solve the linear equation x/3 - 5/6 = 3(x - 3)/12. This problem includes key concepts such as fractions, distributing terms, and solving linear equations. Suitable for students in Grades 8-10.

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