Question

#2
listen
solve the inequality.
-9y < 24
solution:
graph the solution.
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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 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 strict, not "greater than or equal to") and shade to the right. Looking at the graph options, the "open circle pointing right" (the rightmost arrow with an open circle) is used, and we place the open circle at \(-\frac{8}{3}\) (which is between -3 and -2 on the number line) and draw an arrow to the right.

Answer:

The solution to the inequality \(-9y < 24\) is \(y > -\frac{8}{3}\) (or \(y > -2\frac{2}{3}\)). For the graph, use the open - circle arrow pointing to the right (the \(\circ
ightarrow\) option) with the open circle placed at \(y = -\frac{8}{3}\) on the number line and the arrow extending to the right.