Solve the inequality and graph the solution.

Question

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 \( a < 4 \).