Question

Solve the inequality and graph the solution.
a+20
2
<12
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality:

\[
\frac{a + 20}{2} < 12
\]

First, we can eliminate the fraction by multiplying both sides by 2:

\[
a + 20 < 24
\]

Next, we isolate \( a \) by subtracting 20 from both sides:

\[
a < 4
\]

So, the solution to the inequality is:

\[
a < 4
\]

### Step to Graph the Solution

1. **Identify the endpoint:** The endpoint is \( a = 4 \).
2. **Change endpoint from closed to open:** Since our inequality is strict (less than), we will use an open circle on 4.
3. **Graph the solution:** The solution will be represented as an open circle at 4, with a line extending to the left towards negative infinity.

### Graph Representation:
- Draw a number line.
- Put an open circle at \( 4 \) (not filled in).
- Shade the area to the left of \( 4 \) to indicate all numbers less than \( 4 \).

### Summary of the Graph:
- Open circle at \( 4 \)
- Shaded line to the left indicating all numbers less than \( 4 \).

This visually represents the solution \( a < 4 \).