Question

Solve the inequality. Graph and check your solution.

$n+7>3$

Short answer

The solution for the inequality is $n>-4$.

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 Side to 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 $n+7>3$.

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

$\begin{array}{l}n+7>3\\ n+7-7>3-7\\ n>-4\end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $n>-4$

So, this expression means that the value of n should be greater than $-4$.

So, Put $-3,-2,-1,.......so on$in $n+7>3$to check whether the inequality hold or not

Put $n=-3$in inequality,

$\begin{array}{l}n+7>3\\ -3+7>3\\ 4>3\end{array}$

It holds the equation

Again, put $n=-2$in equality

$\begin{array}{l}n+7>3\\ -2+7>3\\ 5>3\end{array}$

It also holds the inequality.

So, the expression $n>-4$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $n>-4$ to get the proper graphical representation to know the points.