Question

graph $x \geq 3$.
-5 -4 -3 -2 -1 0 1 2 3 4 5
switch direction make circle open
how do i graph the inequality?

Explanation:

Step1: Analyze the inequality

The inequality is \( x \geq 3 \). For graphing inequalities on a number line:

• If the inequality is \( \geq \) or \( \leq \), we use a closed (filled) circle at the boundary point because the point itself is included in the solution set.
• If the inequality is \( > \) or \( < \), we use an open circle.
• The direction of the arrow is determined by the inequality: for \( x \geq a \) (where \( a \) is a number), the arrow points to the right (towards larger numbers); for \( x \leq a \), the arrow points to the left (towards smaller numbers).

Step2: Locate the boundary point

The boundary point here is \( x = 3 \). So we first find the position of 3 on the number line.

Step3: Determine the circle type

Since the inequality is \( \geq \), we use a closed (filled) circle at \( x = 3 \).

Step4: Determine the arrow direction

For \( x \geq 3 \), the solution includes all numbers greater than or equal to 3, so the arrow should point to the right (towards numbers larger than 3).

Looking at the given graph, the circle is at -5 which is incorrect. To correct it:

• Move the closed circle to the position of 3 on the number line.
• Then draw the arrow to the right from 3.

Answer:

To graph \( x \geq 3 \):

1. Find \( x = 3 \) on the number line.
2. Draw a closed (filled) circle at \( x = 3 \) (because \( \geq \) includes the boundary point).
3. Draw an arrow pointing to the right (towards numbers greater than 3) from the closed circle at \( x = 3 \).

(The given graph has the circle at -5, which is wrong. The correct graph should have a closed circle at 3 and an arrow to the right.)