Graph Inequalities on a Number Line
Graph Inequalities on a Number Line - How it Works - Video
Example 1
Example 1:
We have x < 17. The first step is to circle the number. Next we have to decide if it is a filled in circle or a closed circle, which means the number is included. Or if it is a empty circle or a open circle, which means the number is not include.
Since we have less than, 17 is not included, so we draw an empty circle or open circle around the number, 17.
Our next step is to decide if we draw the arrow left or right. Next we pick one number to the left of 17 and one number to the right of 17. Since 16 is less than 17 and makes the inequality true, we draw the arrow left.
Example 2
Example 2:
We have x ≥ 4. The first step is to circle the number. Next we have to decide if it is a filled in circle or a closed circle, which means the number is included. Or if it is a empty circle or a open circle, which means the number is not include.
Since we have greater than or equal to, 4 is included, so we draw a filled in circle or closed circle around the number, 4.
Our next step is to decide if we draw the arrow left or right. Next we pick one number to the left of 4 and one number to the right of 4. Since 5 is greater than or equal to 4 and makes the inequality true, we draw the arrow right.
Example 3
Example 3:
We have x ≤ 28. The first step is to circle the number. Next we have to decide if it is a filled in circle or a closed circle, which means the number is included. Or if it is a empty circle or a open circle, which means the number is not include.
Since we have less than or equal to, 28 is included, so we draw a filled in circle or closed circle around the number, 28.
Our next step is to decide if we draw the arrow left or right. Next we pick one number to the left of 28 and one number to the right of 28. Since 24 is less than or equal to 28 and makes the inequality true, we draw the arrow left.
Example 4
| x + 2 | ≥ 16
x + 2 ≥ 16
x ≥ 14
Rewrote the inequality
Drop absolute value signs
Subtract 2 to both sides
| x + 2 | ≤ -16
x + 2 ≤ -16
x ≤ -18
Rewrote the inequality
Drop absolute value signs
Subtract 2 to both sides
Example 4:
We have x > -3. The first step is to circle the number. Next we have to decide if it is a filled in circle or a closed circle, which means the number is included. Or if it is a empty circle or a open circle, which means the number is not include.
Since we have greater than, -3 is not included, so we draw an empty in circle or open circle around the number, -3.
Our next step is to decide if we draw the arrow left or right. Next we pick one number to the left of -3 and one number to the right of -3. Since 0 is greater than -3 and makes the inequality true, we draw the arrow right.