Solve: `x/5+3=(x)/6+12`

Answer

To solve the equation \( \frac{x}{5} + 3 = \frac{x}{6} + 12 \), we will follow these steps:

### Step 1: Write the equation
We start with the equation:
\[ \frac{x}{5} + 3 = \frac{x}{6} + 12 \]

### Step 2: Convert whole numbers to fractions
We can express the whole numbers as fractions:
\[ \frac{x}{5} + \frac{3}{1} = \frac{x}{6} + \frac{12}{1} \]

### Step 3: Find the LCM of the denominators
The least common multiple (LCM) of 5 and 6 is 30. We will multiply each term by 30 to eliminate the fractions:
\[ 30 \left(\frac{x}{5}\right) + 30 \left(\frac{3}{1}\right) = 30 \left(\frac{x}{6}\right) + 30 \left(\frac{12}{1}\right) \]

### Step 4: Simplify the equation
Now, we simplify each term:
\[ 6x + 90 = 5x + 360 \]

### Step 5: Move all \(x\) terms to one side
Subtract \(5x\) from both sides:
\[ 6x - 5x + 90 = 360 \]
This simplifies to:
\[ x + 90 = 360 \]

### Step 6: Isolate \(x\)
Now, subtract 90 from both sides:
\[ x = 360 - 90 \]
This gives us:
\[ x = 270 \]

### Final Answer
The solution to the equation is:
\[ \boxed{270} \]

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