**Answer:**

The equation 3x – 1 = 1 – 3x is a simple linear equation that can be solved to find the value of x. Let’s break it down step by step:

- Start by isolating the x term on one side of the equation. To do this, we can add 3x to both sides of the equation: 3x – 1 + 3x = 1 – 3x + 3xSimplifying the equation gives us: 6x – 1 = 1
- Next, let’s isolate the constant term on the other side of the equation. We can do this by adding 1 to both sides: 6x – 1 + 1 = 1 + 1Simplifying further, we have: 6x = 2
- To solve for x, we need to get rid of the coefficient in front of x. In this case, we have 6 multiplied by x. To undo this multiplication, we can divide both sides of the equation by 6: (6x) / 6 = 2 / 6This simplifies to: x = 1/3

So, the solution to the equation 3x – 1 = 1 – 3x is x = 1/3.

Example:

Let’s substitute x = 1/3 back into the original equation to verify our solution: 3(1/3) – 1 = 1 – 3(1/3)

Simplifying the equation gives us: 1 – 1 = 1 – 1

Both sides of the equation are equal, which confirms that x = 1/3 is indeed the solution to the equation.

To summarize:

- The equation 3x – 1 = 1 – 3x is a linear equation.
- By following the steps mentioned above, we found that the solution to the equation is x = 1/3.
- Substituting the value back into the original equation confirms our solution.

I hope this explanation helps! If you have any further questions, feel free to ask.