Solve the following equations and verify the results.
`(3x-3)/4-(2x-1)/3=1`

Answer

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

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

### Step 2: Find the Least Common Multiple (LCM)
The denominators are 4 and 3. The LCM of 4 and 3 is 12.

### Step 3: Rewrite the equation with the LCM
We will multiply each term by the LCM (12) to eliminate the fractions:
\[ 12 \cdot \left(\frac{3x - 3}{4}\right) - 12 \cdot \left(\frac{2x - 1}{3}\right) = 12 \cdot 1 \]

This simplifies to:
\[ 3(3x - 3) - 4(2x - 1) = 12 \]

### Step 4: Distribute the terms
Now we distribute:
\[ 9x - 9 - 8x + 4 = 12 \]

### Step 5: Combine like terms
Combine the \(x\) terms and the constant terms:
\[ (9x - 8x) + (-9 + 4) = 12 \]
This simplifies to:
\[ x - 5 = 12 \]

### Step 6: Solve for \(x\)
Add 5 to both sides to isolate \(x\):
\[ x = 12 + 5 \]
Thus,
\[ x = 17 \]

### Step 7: Verification
To verify, we substitute \(x = 17\) back into the original equation:
\[ \frac{3(17) - 3}{4} - \frac{2(17) - 1}{3} \]
Calculating each term:
\[ \frac{51 - 3}{4} - \frac{34 - 1}{3} = \frac{48}{4} - \frac{33}{3} \]
This simplifies to:
\[ 12 - 11 = 1 \]
Since both sides of the equation are equal, our solution is verified.

### Final Solution
Thus, the solution to the equation is:
\[ \boxed{17} \]