Question

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: Determine the graph

The solution \(y > -\frac{8}{3}\) means all values greater than \(-\frac{8}{3}\). On a number line, this is represented by an open circle at \(-\frac{8}{3}\) (since \(y\) is not equal to \(-\frac{8}{3}\)) and an arrow pointing to the right (toward larger numbers).

Answer:

The solution to the inequality is \(y > -\frac{8}{3}\) (or \(y > -2\frac{2}{3}\)). For the graph, use the open - circle (hollow dot) pointing to the right (the "o→" icon) placed at \(-\frac{8}{3}\) (or approximately \(-2.67\)) on the number line.