For each inequation , given below, represent the solution on a number line:
`5/2 -2x ge 1/2, x in W`

Answer

To solve the inequality \( \frac{5}{2} - 2x \geq \frac{1}{2} \) and represent the solution on a number line, we will follow these steps:

### Step 1: Write the Inequality
The given inequality is:
\[ \frac{5}{2} - 2x \geq \frac{1}{2} \]

### Step 2: Subtract \( \frac{5}{2} \) from Both Sides
To isolate the term with \( x \), we subtract \( \frac{5}{2} \) from both sides:
\[ \frac{5}{2} - 2x - \frac{5}{2} \geq \frac{1}{2} - \frac{5}{2} \]
This simplifies to:
\[ -2x \geq \frac{1}{2} - \frac{5}{2} \]

### Step 3: Simplify the Right Side
Calculating the right side:
\[ \frac{1}{2} - \frac{5}{2} = \frac{1 - 5}{2} = \frac{-4}{2} = -2 \]
So, we have:
\[ -2x \geq -2 \]

### Step 4: Divide Both Sides by -2
Now, we divide both sides by -2. Remember, when dividing by a negative number, the inequality sign changes:
\[ x \leq 1 \]

### Step 5: Consider the Domain of \( x \)
The problem states that \( x \) belongs to the set of whole numbers (denoted as \( W \)). Whole numbers are \( 0, 1, 2, 3, \ldots \). Therefore, we need to find the whole number solutions that satisfy \( x \leq 1 \).

### Step 6: Identify Valid Solutions
The whole number solutions satisfying \( x \leq 1 \) are:
- \( 0 \)
- \( 1 \)

### Step 7: Represent the Solution on a Number Line
To represent this on a number line:
1. Draw a horizontal line.
2. Mark points for \( 0 \) and \( 1 \).
3. Since \( x \) can be equal to \( 1 \), we will use a solid dot at \( 1 \).
4. We will also use a solid dot at \( 0 \) since \( 0 \) is included in the solution.

The number line will look like this:

```
<---|---|---|---|---|---|---|---|---|--->
-1 0 1 2 3 4 5
● ●
```

### Final Answer
The solution set is \( \{0, 1\} \) represented on the number line with solid dots at \( 0 \) and \( 1 \).

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