Question

Solve the inequality. Graph and check your solution.

$m+8\ge 12$

Short answer

The solution for the inequality is $m\ge 4$.

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 n by solving the inequality

Since, the equality is $m+8\ge 12$.

Here, to simplify this inequality, subtract $-2$ to both side on the above

$\begin{array}{l}m+8\ge 12\\ m+8-8\ge 12-8\\ m\ge 4\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $m\ge 4$.

So, this expression means that the value of m should be greater than or equal to $4$.

So, Put $5,6,7,.........so on$ in $m+8\ge 12$ to check whether the inequality hold or not

Put $m=4$ in inequality,

$\begin{array}{l}m+8\ge 12\\ 4+8\ge 12\\ 12\ge 12\\ 12=12\end{array}$

It holds the equation

Again, put $m=5$ in equality

$\begin{array}{l}m+8\ge 12\\ 5+8\ge 12\\ 13\ge 12\end{array}$

It also holds the inequality.

So, the expression $m\ge 4$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $m\ge 4$ to get the proper graphical representation to know the points.