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
- Identify the endpoint: The endpoint is \( a = 4 \).
- Change endpoint from closed to open: Since our inequality is strict (less than), we will use an open circle on 4.
- 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 \( a < 4 \).