$x \,>\, a$
When two quantities are compared, one quantity can be greater than the second quantity. The comparison between them is denoted by the greater than symbol in mathematics.
Let $a$ and $x$ denote the quantities. Assume that the value of $x$ is greater than $a$, which means they are not equal. So, the inequality between them is written mathematically as follows.
$x > a$
Let’s study this mathematical inequality to understand some properties of the literals $a$ and $x$.
Look at the following arithmetic inequality for better understanding.
$x > 6$
The value of $x$ must be greater than $6$. It means, the value of $x$ can be $7$, $8$, $9$ and so on.
The linear inequality in one variable $x$ greater than $a$ can be represented in three ways in mathematics.
The value of $x$ is not equal to $a$ but every value after $a$ is equal to $x$. However, its last value cannot be determined. Hence, it is denoted by an infinity symbol mathematically.
The value of $x$ is not equal to $a$ and should not be equal to infinity. In other words, every value lies between $a$ and infinity belongs to the variable $x$.
Therefore, the solution set of $x$ is denoted as an open interval between $a$ and infinity.
$x \in (a,\,\infty)$
In this example, the function is $x$ and its value is always greater than the value of $a$. Therefore, the solution set for $x$ greater than $a$ inequality is mathematically expressed in set builder form as follows.
$(1).\,\,\,$ $\{x \,|\, x \,>\, a\}$
$(2).\,\,\,$ $\{x \,:\, x \,>\, a\}$
The $x$ is greater than $a$ linear inequality in one variable can be expressed graphically as per the one-dimensional cartesian coordinate system by a number line.
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