Question

graph the inequality below on the number line. ( a geq 3 )

Explanation:

Step1: Identify the critical point

The inequality is \( a \geq 3 \), so the critical value is \( 3 \). We need to mark this point on the number line. Since the inequality includes equality (\( \geq \)), we use a closed (filled - in) circle at \( 3 \).

Step2: Determine the direction of the line

For the inequality \( a \geq 3 \), we are looking for all values of \( a \) that are greater than or equal to \( 3 \). On the number line, this means we draw an arrow starting from the closed circle at \( 3 \) and pointing to the right (towards positive infinity, or in the direction of increasing numbers on the number line).

Answer:

To graph \( a\geq3 \) on the number line:

1. Locate the number \( 3 \) on the number line.
2. Place a closed (filled) circle at \( 3 \) (because the inequality is "greater than or equal to", so \( 3 \) is included in the solution set).
3. Draw an arrow starting from the closed circle at \( 3 \) and extending to the right (towards \( 4,5,6,\cdots \)) to represent all numbers greater than or equal to \( 3 \).