Inequalities

The relation of inequality between the two values means that the values on either side of the symbol of inequality will not be equal. As the name states, it simply means that both sides of an expression are not equal. Some results are followed in the case when there is inequality in a result. These results can be used to find the solutions to the expression that is given to us. However, all the relations of inequality have the same properties. 

Inequalities Definition

Inequality is a property for which the mathematical expression that is presented to us does not have both of its sides as equal. It means that the left-hand side of the expression will not be equal to the right-hand side of the expression.

The inequality is mainly demonstrated using the ≠ symbol. This symbol means that the facts on both sides of the symbol are not equal. Besides that, any relation can stand true to that expression. However, it surely will not be an equality sign.

This property of an expression is used to define the relationship that one side of the expression holds with the other hand’s side. It means that under the concept of inequality. One side can be greater than the other one, or less than the other one. However, within these two cases, several subcases follow. The basics of the concept will remain the same, however, the difference between both sides of the expression will be demonstrated briefly. To do this, the concept of equality is brought into effect within this topic. It means that there will be a possibility for both sides of the expression to be equal under certain cases even though they are unequal as a whole. 

Inequality Symbols

The most important symbols that comprise the concept of inequality are lesser than, greater than, and not equal to. However, many others can be of much significance in case of certain problems. Some of those symbols are:

• Greater than (>) : This symbol means that the entity that has been represented in the first place ( on the left side of the expression) is greater than the entity on the other side.

a > b

In this, ‘a’ is greater than ‘b’.

• Lesser than (<) : By using this symbol, we relate that the quantity on the left side of this symbol is less than the quantity that has been displayed on the right side of the expression.

a < b

In this, ‘a’ is lesser than ‘b’.

• Not equal to (≠) : We use this symbol to demonstrate that the entities on both sides of the symbol do not have the same solution without using precise calculations. 

a ≠ b

No conditions of lesser than or greater than have been demonstrated. The only thing that is known is that both sides are not equal.

• Lesser or equal to (≤) : If this symbol is used in an expression, then it means that the expression will have two results. One of which is equality and the other one is lesser than.

• Greater or equal to (≥) : This symbol expresses two cases. The two cases are equality and the greater than relation.

Properties of Inequalities

There is a certain set of properties that stand true for any symbol of inequality that is used in an expression. Sona of those properties are as follows;

• Transitivity: this is the relation that is established in the hm three values.

If a ≥ b, and b ≥ c, then a ≥ c

• Addition or subtraction property: If the same value is added to or subtracted from both sides of an inequality expression, the symbol of inequality will remain the same.

If a < b, then a + x < b + x

• Multiplication or division property: If a positive quantity is used to multiply or divide the expression on both sides, then the symbol of inequality remains the same. If the value is negative, then the symbol changes.

If a < b, m < 0, then a × m > b × m

If a < b, m > 0, then a × m < b × m

Conclusion

Each symbol that comes under the concept of inequality has a unique significance to it. Making use of each symbol in the same values will lead to different outcomes every single time. Hence, we must have a basic understanding of the concept of equality and inequality. This concept is useful in drawing the curves or graphs of the straight lines. To find the solution to the expression, some properties related to the topic are utilised. These properties remain the same for each case that comes under the concept of inequality.