Question

This inequality has a  symbol:
                        
But the graph of the solution contains an open circle. 

Explain why the solution does not include x = –2.

Answer 1

we know that
in the expression 3/(x+2) 
for x=-2-------> the denominator is zero

And the denominator cannot be zero, therefore the value of x = -2 can not belong to the domain of the function. That is the reason why the value of x = -2 cannot be included

Answer 2

The denominator never be zero because if the denominator is equal to zero then the function or inequality is not defined, that is x $\neq$ -2.

Given :

$\dfrac{3}{x+2}+4\geq 3$

The following steps can be used in order to graph the solution on the number line:

Step 1 - Write the given inequality.

$\dfrac{3}{x+2}+4\geq 3$

Step 2 - Before simplifying the inequality, remember that denominator never be zero because if the denominator is equal to zero then the function or inequality is not defined, that is:

x + 2 $\neq$ 0

x $\neq$ -2

Step 3 - SImplify the given inequality.

$\rm \dfrac{3}{x+2}\geq -1$

Cross multiply in the above inequality.

$\rm 3\geq -1(x+2)$

Further, simplify the above inequality.

$\rm x\geq -5$

For more information, refer to the link given below:

https://brainly.com/question/24853349