Solve the inequality and graph the solution.

To solve the inequality \( 20 < 12w - 16 \), we first need to isolate the variable \( w \).

1. Add 16 to both sides:

\[ 20 + 16 < 12w \] \[ 36 < 12w \]

2. Now, divide both sides by 12:

\[ \frac{36}{12} < w \] \[ 3 < w \]

This can be rewritten as:

\[ w > 3 \]

Solution

The solution to the inequality is \( w > 3 \).

Graphing the Solution

To graph the solution on a number line:

1. Draw a horizontal line representing all real numbers.
2. Locate the point \( 3 \) on the number line.
3. Since \( w \) is greater than \( 3 \), use an open circle at \( 3 \) to indicate that \( 3 \) itself is not included in the solution.
4. Shade the portion of the number line to the right of \( 3 \) to represent all values greater than \( 3 \).

Here’s a simple representation:

<----o====================>
     3

Where 'o' represents an open circle at \( 3 \), and the shaded line to the right indicates all numbers greater than \( 3 \).