Solve for X: 3=(3x-1)×(1/3) Linear Equation Solution

To solve this problem, we'll follow these steps:

• Step 1: Eliminate the fraction in the given equation by multiplying through by 3.
• Step 2: Solve for $x$ by isolating it on one side of the equation.
• Step 3: Compare the result to the provided answer choices and select the correct one.

Now, let's work through each step:

Step 1: Begin with the given equation:
$3 = (3x - 1) \times \frac{1}{3}$

To eliminate the fraction, multiply both sides by 3:
$3 \times 3 = (3x - 1) \times \frac{1}{3} \times 3$

This simplifies to:
$9 = 3x - 1$

Step 2: Solve for $x$ by isolating it:

Add 1 to both sides to remove the constant term on the right side:
$9 + 1 = 3x - 1 + 1$

Thus, we have:
$10 = 3x$

Finally, divide both sides by 3 to isolate $x$:
$x = \frac{10}{3}$

Step 3: Compare the result to the provided answer choices:

The value $x = \frac{10}{3}$ is equivalent to the mixed number representation $3 \frac{1}{3}$.

Therefore, the solution to the problem is $3\frac{1}{3}$, which matches choice 3.