Solve: `(x)/(2)=(x)/(3)+1`. Check the result.

Answer

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

### Step 1: Eliminate the fractions
To eliminate the fractions, we can find the least common multiple (LCM) of the denominators (2 and 3). The LCM of 2 and 3 is 6. We will multiply every term in the equation by 6.

\[ 6 \cdot \frac{x}{2} = 6 \cdot \left(\frac{x}{3} + 1\right) \]

### Step 2: Distribute the multiplication
Now we distribute the multiplication:

\[ 6 \cdot \frac{x}{2} = 3x \quad \text{(since } 6 \div 2 = 3\text{)} \]
\[ 6 \cdot \frac{x}{3} + 6 \cdot 1 = 2x + 6 \quad \text{(since } 6 \div 3 = 2\text{)} \]

Putting it all together, we have:

\[ 3x = 2x + 6 \]

### Step 3: Isolate the variable
Next, we will isolate \(x\) by subtracting \(2x\) from both sides:

\[ 3x - 2x = 6 \]
\[ x = 6 \]

### Step 4: Check the result
Now we will check our solution by substituting \(x = 6\) back into the original equation:

Left-hand side:
\[ \frac{6}{2} = 3 \]

Right-hand side:
\[ \frac{6}{3} + 1 = 2 + 1 = 3 \]

Since both sides are equal, our solution is verified.

### Final Answer:
The value of \(x\) is \(6\).

---