Solve : `(x-2)/4+1/3=x-(2x-1)/3`

Answer

To solve the equation \((x-2)/4 + 1/3 = x - (2x-1)/3\), we will follow these steps:

### Step 1: Simplify the equation
We start with the equation:
\[ \frac{x-2}{4} + \frac{1}{3} = x - \frac{2x-1}{3} \]

### Step 2: Find a common denominator
The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12. We will multiply every term by 12 to eliminate the fractions:
\[ 12 \cdot \left(\frac{x-2}{4}\right) + 12 \cdot \left(\frac{1}{3}\right) = 12 \cdot \left(x - \frac{2x-1}{3}\right) \]
This simplifies to:
\[ 3(x-2) + 4 = 12x - 4(2x-1) \]

### Step 3: Distribute and simplify
Now we distribute:
\[ 3x - 6 + 4 = 12x - (8x - 4) \]
This simplifies to:
\[ 3x - 2 = 12x - 8x + 4 \]
Which further simplifies to:
\[ 3x - 2 = 4x + 4 \]

### Step 4: Rearrange the equation
Now, we will rearrange the equation to isolate \(x\):
\[ 3x - 4x = 4 + 2 \]
This simplifies to:
\[ -x = 6 \]

### Step 5: Solve for \(x\)
To find \(x\), we multiply both sides by -1:
\[ x = -6 \]

### Final Answer
The solution to the equation is:
\[ \boxed{-6} \]