Hi, I'm having trouble understanding inequality like graphing it on a number line. I don't understand the open circle and close circle. Can someone help explain? Thank you
Of course! I'd be happy to help you understand how to graph inequalities on a number line, including open and closed circles.
When graphing an inequality on a number line, we represent the solutions to that inequality as points on the number line. Inequalities can have different symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Let's explore two common examples:
1. If you have an inequality symbol like < or > (without the line under it), this indicates that the endpoint of the solution is not included. We represent this with an open circle on the number line.
For example, let's graph the inequality x < 3 on a number line.
- Start by drawing a horizontal line, representing the number line.
- Place an open circle (empty circle) on the number 3 because it's not included in the solution.
- Shade the line to the left of the open circle to represent all values less than 3.
2. If you have an inequality symbol like ≤ or ≥ (with the line under it), this indicates that the endpoint of the solution is included. We represent this with a closed circle on the number line.
For example, let's graph the inequality y ≥ -2 on a number line.
- Start by drawing a horizontal line, representing the number line.
- Place a closed circle (filled circle) on the number -2 because it's included in the solution.
- Shade the line to the right of the closed circle to represent all values greater than or equal to -2.
Remember, when graphing inequalities on a number line, we use an open circle for strict inequalities (< or >) where the endpoint is not included, and a closed circle for inclusive inequalities (≤ or ≥) where the endpoint is included. Then, we shade the region to the left or right of the circle based on the inequality's direction.
I hope this explanation helps! Let me know if you have any further questions.