Question

Explain how the graph of $x>5$ is different from the graph of $x\ge 5$.

Short answer

The inclusion of $5$ is the difference between the two graphs.

Step-by-step solution

- Apply the basic concept of linear equalities

Here, use the concept of basic linear inequalities in which we have to know the term inclusion and exclusion of the number which means if a number contains in the equation is $\ge$which the number is also included but if the sign is $>$ which means the number is excluded and in both case equality holds the same.

– Finding the result with the first inequality.

The graph of the above inequality in real line is:

From the graph it is seen that the line of $x>5$, $5$ is not included in the because an open circle is shown at $5$. So, x includes all numbers greater than $5$.

- Finding the result with the second inequality.

The graph of the above inequality in real line is:

From the graph it is seen that the line of$x\ge 5$,$5$ is included in this because an closed circle is shown at \[5\]. So, x includes all numbers greater than or equal to $5$.

-Conclusion for the both case

From the above steps it is clearly seen that the difference in both the inequalities is the inclusion of $5$.