Solve `(2x+3)/(5) gt (4x-1)/(2), x in W`

Answer

To solve the inequality \(\frac{2x + 3}{5} > \frac{4x - 1}{2}\), where \(x\) belongs to the set of whole numbers, we can follow these steps:

### Step 1: Eliminate the fractions by cross-multiplying
We start with the inequality:
\[ \frac{2x + 3}{5} > \frac{4x - 1}{2} \]
Cross-multiplying gives us:
\[ 2(2x + 3) > 5(4x - 1) \]

### Step 2: Distribute on both sides
Distributing the terms, we get:
\[ 4x + 6 > 20x - 5 \]

### Step 3: Rearrange the inequality
Next, we want to get all terms involving \(x\) on one side and the constant terms on the other side. We can subtract \(4x\) from both sides:
\[ 6 > 20x - 4x - 5 \]
This simplifies to:
\[ 6 > 16x - 5 \]

### Step 4: Isolate \(x\)
Now, we add \(5\) to both sides:
\[ 6 + 5 > 16x \]
This simplifies to:
\[ 11 > 16x \]
or
\[ 16x < 11 \]

### Step 5: Divide by 16
Now, we divide both sides by \(16\):
\[ x < \frac{11}{16} \]

### Step 6: Determine whole number solutions
Since \(x\) must be a whole number, we need to find whole numbers that are less than \(\frac{11}{16}\). The value of \(\frac{11}{16}\) is approximately \(0.6875\). The only whole number less than this value is \(0\).

### Conclusion
Thus, the solution for \(x\) in whole numbers is:
\[ x = 0 \]