List the solution set of 50 - 3 (2x - 5) `lt` 25, given that `x in W`. Also, represent the solution set obtained on a number line.

Answer

To solve the inequality \( 50 - 3(2x - 5) < 25 \) and find the solution set for \( x \) in whole numbers, we will follow these steps:

### Step 1: Simplify the inequality
Start with the original inequality:
\[ 50 - 3(2x - 5) < 25 \]
Distribute the \(-3\) inside the parentheses:
\[ 50 - 6x + 15 < 25 \]
Combine like terms:
\[ 65 - 6x < 25 \]

### Step 2: Isolate the variable
Subtract \(65\) from both sides:
\[ -6x < 25 - 65 \]
This simplifies to:
\[ -6x < -40 \]

### Step 3: Divide by -6
When dividing by a negative number, remember to reverse the inequality sign:
\[ x > \frac{-40}{-6} \]
This simplifies to:
\[ x > \frac{40}{6} \]
Which further simplifies to:
\[ x > 6.67 \]

### Step 4: Determine the solution set in whole numbers
Since \(x\) must be greater than \(6.67\) and \(x\) belongs to whole numbers, the smallest whole number satisfying this inequality is \(7\). Therefore, the solution set in whole numbers is:
\[ \{7, 8, 9, 10, \ldots\} \]

### Step 5: Represent the solution set on a number line
To represent this on a number line, we will mark the point \(6.67\) and draw an open circle at this point to indicate that it is not included in the solution. Then, we shade the region to the right of \(6.67\) to represent all whole numbers greater than \(6.67\).

### Final Answer
The solution set is:
\[ \{7, 8, 9, 10, \ldots\} \]
On the number line, it is represented as:
- An open circle at \(6.67\) and shading to the right.

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