If the replacement set is the of whole numbers (W), find the solution set of :
`4x - 2 lt 2x + 10`.

Answer

To solve the inequality \( 4x - 2 < 2x + 10 \) with the replacement set of whole numbers (W), we will follow these steps:

### Step 1: Write the inequality
We start with the given inequality:
\[ 4x - 2 < 2x + 10 \]

### Step 2: Add 2 to both sides
To eliminate the constant on the left side, we add 2 to both sides:
\[ 4x - 2 + 2 < 2x + 10 + 2 \]
This simplifies to:
\[ 4x < 2x + 12 \]

### Step 3: Subtract \( 2x \) from both sides
Next, we subtract \( 2x \) from both sides to isolate the variable \( x \):
\[ 4x - 2x < 12 \]
This simplifies to:
\[ 2x < 12 \]

### Step 4: Divide both sides by 2
Now, we divide both sides by 2 to solve for \( x \):
\[ \frac{2x}{2} < \frac{12}{2} \]
This gives us:
\[ x < 6 \]

### Step 5: Identify the solution set
Since the replacement set is the set of whole numbers (W), which includes \( 0, 1, 2, 3, 4, 5, 6, \ldots \), we need to find all whole numbers that are less than 6. The whole numbers less than 6 are:
\[ 0, 1, 2, 3, 4, 5 \]

### Final Solution Set
Thus, the solution set is:
\[ \{0, 1, 2, 3, 4, 5\} \]