Solve the inequality. Graph and check your solution.

$\frac{p}{7}>6$

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$\frac{p}{7}>6$.

Here, to simplify this inequality, multiply 7 to both side on the above

$\begin{array}{l}\frac{p}{7}>6\\ \frac{p}{7}\times 7>6\times 7\\ p>42\end{array}$

Since, in the expression $p>42$

So, this expression means that the value of p should be greater than $42$.

So, Put $43,44,45,.......so on$ in $\frac{p}{7}>6$ to check whether the inequality hold or not

Put $p=43$ in inequality,

$\begin{array}{l}\frac{p}{7}>6\\ \frac{43}{7}>6\\ 6.1>6\end{array}$

It holds the equation

Again, put $p=44$ in equality

$\begin{array}{l}\frac{p}{7}>6\\ \frac{44}{7}>6\\ 6.2>6\end{array}$

It also holds the inequality.

So, the expression $p>42$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $p>42$ to get the proper graphical representation to know the points.