Solve the inequality $9y+2\left(y+6\right)>5y-24$, graph the solution on the number line, and write the solution in interval notation.

Given inequality is$9y+2\left(y+6\right)>5y-24$

The inequality is to be solved, the solution is to be graphed on the number line, and the solution is to be written in interval notation.

Isolating the variable in the inequality:

$$\begin{gathered} 9y+2\left(y+6\right)>5y-24 \\ 9y+2y+12>5y-24 \\ 11y+12>5y-24 \\ 11y-5y+12-12>5y-5y-24-12 \\ 6y>-36 \\ \frac{6y}{6}>\frac{-36}{6} \\ y>-6 \end{gathered}$$

In an interval notation, a round brackets indicates that the extreme value is excluded and a square bracket indicates that the extreme value is included.

On a number line, if the inequality is less than or greater than then a hollow dot is used to indicate that the number is not included. If the inequality is less than equals or greater than equals then a solid dot is used to indicate that the number is included.

Graphing the interval on a number line: