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

Answer

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

### Step 1: Simplify the Right Side
First, we need to simplify the right side of the equation. We can rewrite \(-1\) as \(-\frac{3}{3}\) to have a common denominator.

\[ \frac{x-2}{3} = \frac{2x-1}{3} - \frac{3}{3} \]

This gives us:

\[ \frac{x-2}{3} = \frac{2x - 1 - 3}{3} \]

Now simplify the numerator on the right side:

\[ \frac{x-2}{3} = \frac{2x - 4}{3} \]

### Step 2: Cross Multiply
Since both sides of the equation have the same denominator (3), we can multiply both sides by 3 to eliminate the denominator:

\[ x - 2 = 2x - 4 \]

### Step 3: Rearrange the Equation
Now, we will rearrange the equation to isolate \(x\). We can move \(2x\) to the left side by subtracting \(2x\) from both sides:

\[ x - 2x = -4 + 2 \]

This simplifies to:

\[ -x = -2 \]

### Step 4: Solve for \(x\)
To find \(x\), we multiply both sides by -1:

\[ x = 2 \]

### Final Answer
Thus, the value of \(x\) is:

\[ \boxed{2} \]

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