Inequalities in Maths: Applications in Real Life Situations

There are many cases in which both sides of an expression separated by a symbol can not be proved to be equal. In those cases, the concept of inequality comes into effect. This concept helps us in finding out the limits that the given expression has and also helps figure out the solutions of the given equation. By finding out the solutions to the equation, it becomes relatively easier for us to plot the graph for these expressions. 

Writing and Using Inequalities

Inequalities are used to limit the values of the entities that are placed alongside them past the inequality symbol. As we know, inequality can be represented in several ways depending on the relation that the values on either side of the inequality symbol carry. 

Example:

x ≥ y

In this expression, it can be seen that the value ‘x’ is greater and equal to ‘y’. It means that all the values of ‘x’ that are greater or equal to the value of ‘y’ will follow this expression. However, it completely neglects the possibility that the value of ‘y’ will ever be greater than ‘x’ for the given expression. 

Hence, inequality gives us a measure of the extent to which there is a difference between the values that are placed on either side of it. 

Similarly, in Mathematics and Physics, it is easy for us to encounter cases when one value is much greater, or much smaller compared to the other. In these cases symbols «, » are used to represent the cast. 

Example:

x « y

This expression demonstrates that the value of ‘y’ far exceeds the value of variable ‘x’. Now, supposedly the difference between both the values can be as much as tens of times. However, the use of this symbol greatly affects the solution of the expression.

How do you use the concepts of inequalities in real life?

The main function of the concept of inequality is to set limits to an expression. This in itself can have a large number of uses in the daily life of a person. You can think of it as setting a limit on your expenditure or budget. And, this will help you keep that within limits or under control.

It helps in identifying the relationship that two things have based on their quantity. If the things are not equal in their quantities, then what is the relation between them? The first object can be greater than the other, it can be lesser, or they can have a greater difference from each other. This all is an account of the property that is possessed by the things due to their inequality. And, that is what the concept of inequality gives an account of.

Why are inequalities in maths important?

The most important purpose that inequality is used for is to solve the expressions or equations. The properties that belong to the expressions that carry a symbol of inequality greatly affect the way an equation can be solved. The symbol of inequality enlarges the prospects in which the equation can give solutions. 

Inequality equations or expressions are used to plot the curves or graphs of the equation that do not carry a certain equality sign. By using the properties of inequality, or simple mathematical operations, we can easily solve the equation to get solutions to those.

Besides, inequality serves a purpose far greater than this one. These symbols greatly emphasise the way an expression can be binomially expanded. Also, in the multiple cases that arise in the concepts of Physics, these symbols play a great role in the calculation of those values. 

These limit the extent to which an expression can be expanded or an equation is solved. Like, in the case of greater or equal inequality, the relation will hold as long as the upper limit of the relation is the same on both sides. Any further than that, the relationship will not stay the same. 

Conclusion

The concept of inequality poses a significant effect on the subject of Mathematics. Without utilising the properties that are possessed by this symbol, it becomes relatively difficult for us to find the solutions to all the equations. However, when we utilise the basics that belong to this concept, we can easily solve the equation to get their solutions and graphs. Besides, these are also helpful in the expansion of equations to higher powers. That is why it is necessary to have a basic understanding of this topic to be able to solve equations more effectively.