Question

#2
solve the inequality.
-9y < 24
solution:
graph the solution.

Explanation:

Step1: Divide both sides by -9

When dividing an inequality by a negative number, the inequality sign flips. So, divide both sides of \(-9y < 24\) by \(-9\):
\(y > \frac{24}{-9}\)
Simplify \(\frac{24}{-9}\) to \(-\frac{8}{3}\) (or approximately \(-2.666...\)).

Step2: Interpret the solution

The solution to the inequality is \(y > -\frac{8}{3}\) (or \(y > -2\frac{2}{3}\)). For graphing, since the inequality is "greater than" (not "greater than or equal to"), we use an open circle at \(-\frac{8}{3}\) (or \(-2.666...\)) and an arrow pointing to the right (toward larger numbers).

Answer:

The solution to the inequality \(-9y < 24\) is \(y > -\frac{8}{3}\) (or \(y > -2\frac{2}{3}\)). For the graph, use an open circle at \(-\frac{8}{3}\) (near \(-2.67\)) and an arrow pointing to the right (e.g., the "open circle with right arrow" option in the graph tools).