If `5-(2)/(x)=2-(5)/(x),` then `|(x)/(3)|=`

Answer

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

### Step 1: Rearrange the equation
Start by moving all terms involving \( x \) to one side and the constant terms to the other side.

\[ 5 - 2 = \frac{2}{x} - \frac{5}{x} \]

### Step 2: Simplify both sides
This simplifies to:

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

### Step 3: Combine the fractions
The right-hand side can be simplified further:

\[ 3 = \frac{-3}{x} \]

### Step 4: Cross-multiply
To eliminate the fraction, we can cross-multiply:

\[ 3x = -3 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 3:

\[ x = -1 \]

### Step 6: Find \( \left| \frac{x}{3} \right| \)
Now we need to find \( \left| \frac{x}{3} \right| \):

\[ \left| \frac{-1}{3} \right| = \frac{1}{3} \]

### Final Answer
Thus, the value of \( \left| \frac{x}{3} \right| \) is:

\[ \frac{1}{3} \]

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