Question

What are the most five common inequality symbols?

Answer 1

Inequality symbols are visual representations of inequality relationships. They are often referred to as relation symbols, along with other mathematical symbols such as the equals sign (=), which implies an equality relation.
Less than ($\mathrm{<}$) and greater than ($\mathrm{>}$) symbols are examples of strict inequalities. While an equal sign is not technically an inequality symbol, it is used in non-strict inequalities like greater than or equal to and less than or equal to ($\le$).

Complete step by step solution:
The most five common inequality symbols are
$\ne$=not equal To
$\mathrm{>}$= greater than
$\mathrm{<}$=less than
$\ge$=greater than or equal to
$\le$=less than or equal to
Let us discuss each inequality symbol in detail.
1.not equal to sign: ($\ne$)
The not equal sign, also known as the does not equal sign, is a symbol that means that the values or expressions on either side of the symbol are unequal.
For example,
$12\ne5$
$x-8\ne x+8$
$y^{2} \ne y^{3}$
Although the above use shows us that the terms on both sides of the symbol are not identical, it doesn't tell us anything else. Other, more complex inequality relations exist, such as the ones mentioned below.
2.greater than: ($>$)
The greater than sign is a symbol that denotes a strict inequality between two values; that is, the value to the left of the greater than sign is greater than the value to the right. it is a strict inequality, which means that the value on the left must be greater than the value on the right; they cannot be equal. The greater than sign can be used in the following ways:
$8>6$
$x^{2} >x$
3.Greater than or equal to sign: ($\ge$)
The greater than or equal sign denotes that the value on the left side of the symbol is greater than or equal to the value on the right. This can also be read as the left-hand value is at least equal to the right-hand value.
Given,
$a\ge b$
a should be equal to b , unlike the greater than sign. Hence, $\ge$ is not a strict inequality.
4.less than sign ($<$)
The reverse of the greater than sign is the less than sign. The value on the left of the less than sign is greater than the value on the right, suggesting a strict inequality between two values. The less than symbol can be used in the following ways:
$6<144$
$x-7< x^{2}$
5.less than or equal to ($\le$)
The less than or equal sign signifies that the value on the left side of the symbol is less than or equal to the value on the right. This can also be interpreted to mean that the value or expression on the left-hand side of the symbol can only be equal to, and never greater than, the value on the right. In most cases, it is given as
$a\le b$
a should be equal to b, unlike the less than sign. Hence, $\le$ is not a strict inequality.

Note: The mistake done by the students is not understanding the difference between the symbols and sometimes gets confused about choosing the best inequality symbol between the required numbers.