Question

Solve the inequality. Graph and check your solution.

$-6s\le 54$

Short answer

The solution for the inequality is $s\le -9$.

Step-by-step solution

Step -1 - Apply the concept of Linear inequalities

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.

Step -2 – Find the value of s by solving the inequality

Since, the equality is $-6s\le 54$.

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

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

Step- 3 - Check the expression to verify the inequality

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.