Solve the inequality. Graph and check your solution.

$-6s\le 54$

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 $-6s\le 54$.

Here, to simplify this inequality, divide $6$to both side on the above

$\begin{array}{l}-6s\le 54\\ \frac{-6s}{-6}\le \frac{54}{-6}\\ s\le -9\end{array}$

Since, in the expression $s\le -9$

So, this expression means that the value of s should be smaller than or equal to $-9$.

So, Put $-8,-7,-6,.......so on$in $-6s\le 54$to check whether the inequality hold or not

Put $s=-8$in inequality,

role="math" localid="1647847769099" $\begin{array}{l}-6s\le 54\\ -6\times -8\le 54\\ 48\le 54\end{array}$

It holds the equation

Again, put $s=-7$in equality

$\begin{array}{l}-6s\le 54\\ -6\times -7\le 54\\ 42\le 54\end{array}$

It also holds the inequality.

So, the expression $s\le -9$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $s\le -9$ to get the proper graphical representation to know the points.