Solve: `(2x)/(5)-(x)/(2)=(5)/(2)`.

Answer

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

### Step 1: Find the Least Common Multiple (LCM)
The denominators in the equation are 5 and 2. The LCM of 5 and 2 is 10.

### Step 2: Rewrite each term with the LCM
We will rewrite each term in the equation using the LCM:
\[ \frac{2x}{5} = \frac{2x \cdot 2}{5 \cdot 2} = \frac{4x}{10} \]
\[ \frac{x}{2} = \frac{x \cdot 5}{2 \cdot 5} = \frac{5x}{10} \]
\[ \frac{5}{2} = \frac{5 \cdot 5}{2 \cdot 5} = \frac{25}{10} \]

Now, substitute these back into the equation:
\[ \frac{4x}{10} - \frac{5x}{10} = \frac{25}{10} \]

### Step 3: Combine the fractions
Now that we have a common denominator, we can combine the left side:
\[ \frac{4x - 5x}{10} = \frac{25}{10} \]
This simplifies to:
\[ \frac{-x}{10} = \frac{25}{10} \]

### Step 4: Eliminate the denominator
To eliminate the denominator, we can multiply both sides of the equation by 10:
\[ -x = 25 \]

### Step 5: Solve for \(x\)
Now, to solve for \(x\), we multiply both sides by -1:
\[ x = -25 \]

### Final Answer:
The solution to the equation is:
\[ x = -25 \]