Question

graph the inequality below on the number line.
(a > -8)
(there is a number line with marks from -11 to 11)

Explanation:

Step1: Identify the critical point

The inequality is \( a > -8 \), so the critical value is \(-8\). Since the inequality is "greater than" (not "greater than or equal to"), we use an open circle at \(-8\) to show that \(-8\) is not included in the solution set.

Step2: Determine the direction of the line

For \( a > -8 \), the solutions are all numbers greater than \(-8\). On the number line, this means we draw an arrow starting from the open circle at \(-8\) and pointing to the right (towards positive infinity, or increasing values).

To graph it:

1. Locate \(-8\) on the number line.
2. Draw an open circle at \(-8\) (because \( a \) is strictly greater than \(-8\), not equal to it).
3. Draw a line (or arrow) starting from the open circle at \(-8\) and extending to the right (passing through \(-7, -6, \dots, 0, 1, 2, \dots\)) to represent all values of \( a \) that are greater than \(-8\).

Answer:

To graph \( a > -8 \):

• Place an open circle at \(-8\) (since \( a

eq -8 \)).

• Draw an arrow starting at the open circle and pointing to the right (towards values greater than \(-8\)) along the number line.

(Visually, on the given number line: open circle at \(-8\), arrow pointing right past \(-7, -6, \dots, 10, 11, \dots\))