**Solving the Equation: 6x + 1/3 + 1 = x - 3/6**

In this article, we will solve the given equation step by step.

**The Equation:**

6x + 1/3 + 1 = x - 3/6

**Step 1: Simplify the Equation**

To simplify the equation, we will start by combining the like terms.

6x + 1/3 + 1 = x - 3/6

First, let's combine the fractions:

1/3 + (-3/6) = 2/6 + (-3/6) = -1/6

So, the equation becomes:

6x + 1 = x - 1/6

**Step 2: Isolate the Variable (x)**

Now, let's isolate the variable x.

6x - x = -1/6 - 1

This simplifies to:

5x = -7/6

**Step 3: Solve for x**

To solve for x, we will multiply both sides of the equation by 6 to eliminate the fraction:

5x = -7/6

Multiplying both sides by 6:

30x = -7

Dividing both sides by 5:

x = -7/30

x = -7/30

**The Solution:**

Therefore, the solution to the equation 6x + 1/3 + 1 = x - 3/6 is x = -7/30.