Open circle for -x + 1 - 8. Closed circle for 2x + 7 + 2 ≤ 9.
To determine which inequalities use an open circle, we need to analyze the signs of the inequality and the variable coefficient.
x + 1 - 8:
The variable coefficient (-1) is negative.
The inequality sign (<) indicates the solution is less than a certain value.
Since the variable coefficient is negative and the inequality sign is less than, the solution excludes the endpoint. This means we should use an open circle to represent this inequality on the number line.
2x + 7 + 2 ≤ 9:
Variable coefficient (2) is positive.
The inequality sign (≤) indicates the solution is less than or equal to a certain value.
When the variable coefficient is positive and the inequality sign includes "equal to," the solution includes the endpoint. Therefore, we should use a closed circle to represent this inequality on the number line.
In conclusion, the inequality **-x + 1 - 8** would be graphed using an open circle.
Question:
Which two of the following inequalities would be graphed on a number line by using an open circle?
-x + 1 -8
2x + 7 + 2 ≤ 9