Solve: `7y - 3 le 2y + 14`, `y in W`.

Options

A. `0,1,2`
B. `1,2,3`
C. `0,1,2,3`
D. `1,2,3,4`

Answer

To solve the inequality \( 7y - 3 \leq 2y + 14 \) where \( y \) belongs to the set of whole numbers \( W \), we will follow these steps:

### Step 1: Rearranging the Inequality
Start by moving all terms involving \( y \) to one side and constant terms to the other side.

\[ 7y - 3 \leq 2y + 14 \]

Subtract \( 2y \) from both sides:

\[ 7y - 2y - 3 \leq 14 \]

### Step 2: Simplifying the Terms
Now, simplify the left side:

\[ 5y - 3 \leq 14 \]

### Step 3: Isolate the Variable
Next, add 3 to both sides to isolate the term with \( y \):

\[ 5y \leq 14 + 3 \]

\[ 5y \leq 17 \]

### Step 4: Solve for \( y \)
Now, divide both sides by 5 to solve for \( y \):

\[ y \leq \frac{17}{5} \]

### Step 5: Convert to Decimal
Convert \( \frac{17}{5} \) to a decimal for better understanding:

\[ \frac{17}{5} = 3.4 \]

### Step 6: Identify Whole Number Solutions
Since \( y \) must be a whole number (i.e., \( y \in W \)), we consider whole numbers less than or equal to 3.4. The whole numbers satisfying this condition are:

\[ y = 0, 1, 2, 3 \]

### Final Solution
Thus, the values of \( y \) that satisfy the inequality are:

\[ \{0, 1, 2, 3\} \]

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