Sure! Let me explain what the equation 3x – 1 = 1 – 3x means and how to solve it step by step.

The equation 3x – 1 = 1 – 3x is a linear equation in one variable (x). Solving this equation will help us find the value of x that satisfies the equation. Here’s how we can do it:

- Start by simplifying the equation: 3x – 1 = 1 – 3x
- Group the x terms on one side and the constant terms on the other side: 3x + 3x = 1 + 1
- Combine like terms: 6x = 2
- Divide both sides of the equation by 6 to isolate x: x = 2/6
- Simplify the fraction: x = 1/3

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

To further illustrate the solution, let’s substitute the value of x back into the original equation and check if it holds true:

3(1/3) – 1 = 1 – 3(1/3) 1 – 1 = 1 – 1 0 = 0

As we can see, both sides of the equation are equal when x = 1/3, which confirms that our solution is correct.

In summary:

- The equation 3x – 1 = 1 – 3x is a linear equation in one variable.
- To solve it, we need to isolate the variable (x) on one side of the equation.
- By simplifying and performing necessary operations, we found that x = 1/3 satisfies the equation.
- Substituting the value of x back into the equation confirms our solution.

I hope this explanation clarifies the meaning of the equation and how to solve it. If you have any further questions, feel free to ask!