How do you change the subject of the formula y = 3x + 2 to x?

To change the subject of the formula \( y = 3x + 2 \) to \( x \), rearrange it to \( x = \frac{y - 2}{3} \).

First, let's start by isolating the term that contains \( x \). The original equation is \( y = 3x + 2 \). To isolate \( 3x \), we need to get rid of the constant term on the right-hand side. We do this by subtracting 2 from both sides of the equation. This gives us:

\[ y - 2 = 3x \]

Now, we have \( 3x \) on one side of the equation and everything else on the other side. The next step is to isolate \( x \) itself. Since \( x \) is being multiplied by 3, we need to do the opposite operation to both sides of the equation, which is division. Divide both sides by 3:

\[ \frac{y - 2}{3} = x \]

To make it look more standard, we can write it as:

\[ x = \frac{y - 2}{3} \]

And there you have it! The subject of the formula has been changed from \( y \) to \( x \). This process involves basic algebraic operations: subtraction and division. By following these steps, you can rearrange many similar equations to solve for different variables.