Non-strict inequality

A relation that expresses the comparison between the combination of both unequal and equal quantities is called non-strict inequality.

Introduction

A quantity is compared with at least two quantities in mathematics to know how different a quantity is from other quantities. Sometimes, one quantity is equal to one of them but different to the remaining quantity. In this case, the comparison of the quantities represents both equality and inequality.

Due to the equality property of the quantities, the mathematical relation is not an inequality strictly but it is considered as an inequality due to the inequality property of the quantities. Hence, this type of mathematical relations is called a non-strict inequality.

Greater than or equal

In this case, the value of $x$ is equal to $4$ and the value of $x$ is also greater than $4$. It means, the value of $x$ should be at least $4$.

$x \,=\, 4$
$x \,>\, 4$

Look at the both cases, one case expresses an equation but other case expresses an inequality.

The combination of both equation and inequality is not strictly an inequality but it is considered as an inequality due to the involvement an inequality. It is written as $x \ge 4$ in mathematics.

In general, it is written as $x \ge a$ algebraically in mathematics. It is called a Non-strict inequality.

Less than or equal

In this case, the value of $x$ is equal to $-1$ and also less than $-1$. It means, the value of $x$ should be minimum $-1$.

$x \,=\, -1$
$x \,<\, -1$

Observe the above case, one relation is an equation and other mathematical relation is an inequality. Hence, it is considered as an inequality. It is written as $x \,\le\, -1$. Algebraically, it is written as $x \le a$ in mathematics.