Solve the inequality. Graph and check your solution.

$\frac{t}{4}\le -9$

In this type of inequality, Simply use the property of addition or subtraction or multiplication or division of suitable number on both Left Hand Side & Right Hand Sideto maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Since, the equality is $\frac{t}{4}\le -9$.

Here, to simplify this inequality, multiply $4$to both side on the above

Since, in the expression $t\le -36$

So, this expression means that the value of t should be smaller than or equal to $-36$.

So, Put $-37,-38,-39,.......so on$ in $\frac{t}{4}\le -9$ to check whether the inequality hold or not

Put $t=-37$ in inequality,

$\begin{array}{l}\frac{t}{4}\le -9\\ \frac{-37}{4}\le -9\\ -9.1\le -9\end{array}$

It holds the equation

Again, put in equality

$\begin{array}{l}\frac{t}{4}\le -9\\ \frac{-38}{4}\le -9\\ -9.2\le -9\end{array}$

It also holds the inequality.

So, the expression$t\le -36$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression$t\le -36$ to get the proper graphical representation to know the points.