Question

Solve the inequality and graph the solution.
20<12w–16

Answer 1

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 \( 3 \).