Question

Solve the inequality. Graph and check your solution.

$x+2>-3$

Short answer

The solution for the inequality is $x>-5$.

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 x by solving the inequality

Since, the equality is $x+2>-3$.

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

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

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x>-5$

So, this expression means that the value of x should be greater than $-5$.

So, Put $-4,-3,-2,.........so on$in $x+2>-3$to check whether the inequality hold or not

Put $x=-4$ in inequality,

$\begin{array}{l}x+2>-3\\ -4+2>-3\\ -2>-3\end{array}$

It holds the equation

Again, put $x=-3$in equality

$\begin{array}{l}x+2>-3\\ -3+2>-3\\ -1>-3\end{array}$

It also holds the inequality.

So, the expression $x>-5$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $x>-5$ to get the proper graphical representation to know the points.