Inequalities vs Equations: Difference and Comparison

Inequalities represent the comparative evaluation of the variables on the left to those on the right of the ‘<’ or ‘>’ sign. Alternatively, equations represent the equality of the variables on the left and right sides of the ‘=’ sign.

Inequalities compare the relative size of values, while equations prove them to be equal. This seminal difference also gives rise to other differences that must be cognized.

Key Takeaways

  1. Equations are mathematical statements that assert the equality of two expressions; inequalities indicate a relationship of greater than, less than, or not equal between two expressions.
  2. Equations can have a finite number of solutions; inequalities can have infinite solutions.
  3. Equations represent a specific point or value; inequalities represent a range of values that satisfy the statement.

Inequalities vs. Equations

An equation is a statement that shows the equality between two expressions to find the values of the variables that make the equation true. An inequality is a statement that shows a relationship between two expressions that are not necessarily equal and is used to compare the values of two variables.

Inequalities vs Equations

Comparison Table

Parameters of ComparisonInequalitiesEquations
DefinitionIt is a mathematical statement that represents the inequality and order of variables on the left and right sides.It is a mathematical statement representing the equality between an equation’s left and right side variables.
Symbols UsedThe ‘greater than’ and ‘lesser than’ signs symbolically represent the relationship between variables.The ‘equal to’ sign is used to represent the relationship between variables. symbolically
Representational FunctionRepresent inequality between the variables used.Represent equality between the variables used.
SolutionsA solution set -with infinite answers- is a plausible result for an inequality.The solution for an equation is fixed and singular.
Number of RootsThe total number of roots for inequalities is infinite.The total number of roots for equations is definite.

What are Inequalities?

Inequalities are mathematical statements that represent the unequal relationship between a set of variables. They employ the ‘>’ or ‘<’ signs to signify the comparative analysis of the variables used.

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Inequalities necessarily represent the order of the relationship between the variables used.

They are also used in mathematical problems to compare the relative size of values. Inequalities can be presented in two ways.

Their presentation may have a close semblance to equations or be a simple statement of fact- like in mathematical theorems. Inequalities are commonly used to compare integers, variables, and other algebraic expressions.

Some examples of inequalities are:

‘c > d’, where ‘c’ is greater than ‘d’.

‘c < d’, where ‘c’ is lesser than ‘d’.

There can be several variants among inequalities, including strict and compound inequalities. Each of these variants has a given set of rules to determine the resultant solution set.

What are Equations?

Equations are also mathematical statements representing the equality of variables on the left and right sides of the statement. They use the ‘=’ sign to represent the equality of the values of the two given sets of algebraic variables.

In an equation, the solution is always unitary and representative of the equality between the left and right sides.

Some examples of equations are:

a + 2 = 30, where ‘a + 2’ and ‘30’ are both algebraic expressions, separated by the ‘=’ sign.

5a + 5 = 35, where ‘5a + 5’ and ‘35’ are both algebraic expressions, separated by the ‘=’ sign.

Commonly, equations include more than one variable. In the examples above, solving the equation refers to finding out the value of the unknown variable. Equations are used extensively in algebraic calculations.

Equations can also be of various types, like linear, simultaneous, and quadratic equations.

equations

Main Differences Between Inequalities and Equations

  1. The main difference between inequalities and equations is their definitions that delineate their functionalities in mathematical operations. As the name suggests, an equation represents the equality between two variables in the given formulation.
    The left side of an equation is invariably equal to the right side. Inequalities, on the other hand, are mathematical statements of the inequality between variables. The left and right sides of inequalities represent variables as greater than or less than- highlighting their inequality and relative sizes.
  2. The second seminal difference between the two is what they each represent. While inequalities connote the inequality between two variables, equations represent the equality between two variable quantities.
  3. The symbols used to express equality and inequality in each of these are also different. Inequalities utilize ‘>’ and ‘<’ symbols to represent the inequality between variables, while equations represent equality between given variables by using alphabetical symbols like ‘a’ and ‘b’ accompanied by the mandatory ‘equal to’ sign between the left and right sides.
    Inequality signs are used in the former, while equality signs are implemented in the latter.
  4. Inequalities and equations are also significantly different in terms of their potential solutions. Multiple answers may be possible for inequalities. A ‘solution set’- comprising infinite values- is prescribed as a befitting solution for inequality. On the other hand, only one answer can be determined for an equation.
  5. Lastly, the total number of roots of an equation is definite. This is not the case for inequalities.
Difference Between Inequalities and Equations
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References
  1. https://ieeexplore.ieee.org/abstract/document/754846/
  2. http://www.mathematik.uni-dortmund.de/~erme/CERME4/CERME4_WG6.pdf#page=24
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Last Updated : 11 June, 2023

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20 thoughts on “Inequalities vs Equations: Difference and Comparison”

  1. The comparisons drawn between inequalities and equations in this article are both lucid and thought-provoking. It’s an enriching read.

    Reply
    • Absolutely, the article’s elucidation of these concepts significantly contributes to the understanding of mathematical relationships.

      Reply
  2. I found the examples of inequalities and equations provided in the article very helpful in illustrating the concepts being discussed.

    Reply
  3. The article effectively delves into the nuances of inequalities and equations, providing a well-rounded understanding of these fundamental mathematical principles.

    Reply
  4. The distinction between inequalities and equations is clearly explained in this article, making it a valuable resource for mathematics education.

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  5. The article provides a comprehensive and detailed comparison of inequalities and equations. It’s a great resource for anyone wanting to deepen their understanding of these mathematical concepts.

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  6. The way the article distinguishes between inequalities and equations is both insightful and educational. It’s an excellent resource for mathematics students and enthusiasts.

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    • Absolutely, the article’s detailed exploration of these concepts is incredibly beneficial for anyone seeking a deeper understanding of mathematical relationships.

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  7. The article’s comparison table effectively summarizes the key differences between inequalities and equations, making it easier to comprehend the nuances of each concept.

    Reply
    • I particularly appreciate the detailed analysis of the comparison table. It helps clarify the distinctions between these mathematical expressions.

      Reply
  8. The examples of inequalities and equations are presented in a way that facilitates better understanding of both concepts. It’s a well-structured article overall.

    Reply
    • Definitely, the clarity in the examples used contributes to the article’s value in explaining these mathematical concepts.

      Reply
  9. Inequalities and equations are fundamental concepts in mathematics, and this article does an excellent job of explaining the crucial differences between the two. Very informative!

    Reply

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