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 \(-9\):
\(y > \frac{24}{-9}\)

Step2: Simplify the fraction

Simplify \(\frac{24}{-9}\) by dividing numerator and denominator by their greatest common divisor, which is 3:
\(\frac{24\div3}{-9\div3} = \frac{8}{-3}=-\frac{8}{3}\approx -2.67\)
So the solution is \(y > -\frac{8}{3}\) (or \(y > -2\frac{2}{3}\)).

For graphing: Since the inequality is \(y > -\frac{8}{3}\), we use an open circle at \(-\frac{8}{3}\) (because the inequality is "greater than," not "greater than or equal to") and draw an arrow to the right (indicating all values greater than \(-\frac{8}{3}\)).

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 \(-\frac{8}{3}\) (or approximately \(-2.67\)) and an arrow pointing to the right.