If `(2x-1)/3=(x-2)/3+1`, Then `x=?`

Options

A. `2`
B. `4`
C. `6`
D. `8`

Answer

To solve the equation \(\frac{2x - 1}{3} = \frac{x - 2}{3} + 1\), we will follow these steps:

### Step 1: Eliminate the fractions
Multiply both sides of the equation by 3 to eliminate the denominators:

\[ 3 \cdot \frac{2x - 1}{3} = 3 \cdot \left(\frac{x - 2}{3} + 1\right) \]

This simplifies to:

\[ 2x - 1 = x - 2 + 3 \]

### Step 2: Simplify the right side
Now, simplify the right side of the equation:

\[ 2x - 1 = x - 2 + 3 \]

Combine the constants on the right:

\[ 2x - 1 = x + 1 \]

### Step 3: Rearrange the equation
Next, we will move all terms involving \(x\) to one side and constant terms to the other side. Subtract \(x\) from both sides:

\[ 2x - x - 1 = 1 \]

This simplifies to:

\[ x - 1 = 1 \]

### Step 4: Solve for \(x\)
Now, add 1 to both sides to isolate \(x\):

\[ x = 1 + 1 \]

Thus, we find:

\[ x = 2 \]

### Final Answer
The value of \(x\) is \(2\).

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