Question

Solve the inequality. Graph and check your solution.

$z-15>72$

Short answer

The solution for the inequality is $z>87$.

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 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 d by solving the inequality

Since, the equality is $z-15>72$.

Here, to simplify this inequality, adding $15$ to both side on the above

$\begin{array}{l}z-15>72\\ z-15+15>72+15\\ z>87\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $z>87$.

So, this expression means that the value of z should be greater than $87$.

So, Put $88,89,90,.........so on$ in $z-15>72$to check whether the inequality hold or not

Put $z=88$ in inequality,

$\begin{array}{l}z-15>72\\ 88-15>72\\ 73>72\end{array}$

It holds the equation

Again, put $z=89$ in equality

$\begin{array}{l}z-15>72\\ 89-15>72\\ 74>72\end{array}$

It also holds the inequality.

So, the expression $z>87$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $z>87$ to get the proper graphical representation to know the points.