Solve `9x-7 le 28 +4x, x in W`.

Answer

To solve the inequality \( 9x - 7 \leq 28 + 4x \) where \( x \) belongs to whole numbers, we will follow these steps:

### Step 1: Rearrange the inequality
First, we need to get all the terms involving \( x \) on one side and the constant terms on the other side. We do this by subtracting \( 4x \) from both sides and adding \( 7 \) to both sides.

\[ 9x - 4x - 7 \leq 28 \]

Adding \( 7 \) to both sides gives:

\[ 9x - 4x \leq 28 + 7 \]

### Step 2: Simplify the inequality
Now, simplify both sides:

\[ 5x \leq 35 \]

### Step 3: Solve for \( x \)
Next, we divide both sides by \( 5 \) to isolate \( x \):

\[ x \leq \frac{35}{5} \]

Calculating the right side gives:

\[ x \leq 7 \]

### Step 4: Determine the solution set
Since \( x \) must be a whole number, the possible values for \( x \) that satisfy this inequality are:

\[ x = 0, 1, 2, 3, 4, 5, 6, 7 \]

### Final Solution
Thus, the solution set is:

\[ \{0, 1, 2, 3, 4, 5, 6, 7\} \]

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