Solve: `x/3-2=(x)/4+5`

Answer

To solve the equation \( \frac{x}{3} - 2 = \frac{x}{4} + 5 \), we will follow these steps:

### Step 1: Move all terms involving \( x \) to one side and constant terms to the other side.
We can start by adding \( \frac{x}{4} \) to both sides and adding \( 2 \) to both sides.

\[ \frac{x}{3} - 2 + 2 = \frac{x}{4} + 5 + 2 \]

This simplifies to:

\[ \frac{x}{3} = \frac{x}{4} + 7 \]

### Step 2: Eliminate the fractions by finding a common denominator.
The least common multiple (LCM) of the denominators \( 3 \) and \( 4 \) is \( 12 \). We will multiply every term in the equation by \( 12 \) to eliminate the fractions.

\[ 12 \cdot \frac{x}{3} = 12 \cdot \frac{x}{4} + 12 \cdot 7 \]

This simplifies to:

\[ 4x = 3x + 84 \]

### Step 3: Isolate \( x \).
Now, we will subtract \( 3x \) from both sides:

\[ 4x - 3x = 84 \]

This simplifies to:

\[ x = 84 \]

### Final Answer:
The solution to the equation is \( x = 84 \).

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