Differences between inequalities and equations with table. The difference between inequalities and equations It is in terms of their definitions that in turn influence their use in mathematical problems. While inequalities are used to represent the unequal relationship between a set of variables, equations are used to symbolically represent the equality of the two sets of variables used.
The inequalities represent the comparative evaluation of the variables on the left with those on the right of the ‘<‘ or ‘>’ sign. Alternatively, the 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 they are equal. This fundamental difference also gives rise to a number of other differences that must be recognized.
Comparison table between inequalities and equations
|Definition||It is a mathematical statement representing the inequality and order of the variables on the left and right sides.||It is a mathematical statement that represents the equality between the variables on the left and right side in an equation.|
|Symbols used||The signs ‘greater than’ and ‘less than’ are used to symbolically represent the relationship between variables.||The ‘equal to’ sign is used to symbolically represent the relationship between variables|
|Representative function||Represents the inequality between the variables used.||Represents the equality between the variables used.|
|Solutions||A set of solutions – with infinite answers – is a plausible result for an inequality.||The solution of an equation is fixed and singular.|
|Number of Roots||The total number of roots of the inequalities is infinite.||The total number of roots of the equations is defined.|
What are inequalities?
Inequalities are mathematical statements that represent the unequal relationship between a set of variables. They use the signs ‘>’ or ‘<‘ to indicate the comparative analysis of the variables used. The inequalities necessarily represent the order of the relationship between the variables used.
They are also used in math problems to compare the relative size of values. Inequalities can be presented in two ways.
Their presentation can have a strong resemblance to equations or they can also be presented as a simple statement of facts, as in mathematical theorems. Inequalities are commonly used to compare whole numbers, variables, and other algebraic expressions.
Some examples of inequalities are:
‘c> d’, where ‘c’ is greater than ‘d’.
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There can be a number of variants between inequalities, including strict and compound ones. Each of these variants has a given set of rules to determine the resulting set of solutions.
What are equations?
Equations are also mathematical statements that are used to represent 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 algebraic expressions, separated by the ‘=’ sign.
5a + 5 = 35 , where ‘5a + 5 ′ and’ 35 ‘are algebraic expressions, separated by the’ = ‘sign.
Equations generally include more than one variable. In the examples given above, the process of solving the equation refers to finding the value of the unknown variable. The equations are widely used in algebraic calculations.
Equations can also be of various types, such as linear and simultaneous equations and quadratic equations.
Main differences between inequalities and equations
- The main difference between inequalities and equations is in terms of their definitions that clearly delineate their functionalities in mathematical operations. An equation – as the name suggests – 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 the inequalities represent variables as greater or less than, highlighting their inequality and relative sizes.
- The second fundamental difference between the two is in terms of what each represents. While inequalities connote inequality between two variables, equations are used to represent equality between two variable quantities.
- The symbols used to express equality and inequality in each of these are also different. Inequalities use symbols ‘>’ and ‘<‘ to represent inequality between variables, while equations represent equality between given variables by using alphabetic symbols such as ‘a’ and ‘b’ accompanied by the mandatory sign ‘equal to’ between the left and right sides. Inequality signs are used in the former, while equality signs are implemented in the latter.
- The inequalities and equations are also significantly different in terms of their possible solutions. Multiple answers may be possible for inequalities. A ‘set of solutions’, comprising infinite values, is prescribed as a suitable solution for an inequality. On the other hand, only one answer can be determined for an equation.
- Finally, the total number of roots of an equation is defined. This is not the case for inequalities.
Both inequalities and equations are fairly common mathematical statements that are used to represent the relationship between a set of variables. Although both are solved using similar techniques, there are fundamental differences between the two that should be known.
The most important difference between the two is in terms of the type of representation that each offers to the variables used. While the inequalities represent the unequal relationship between the two variables in the mathematical statement, the equations represent the equality between the variables.
Both mathematical statements use different symbols to express the relationship between variables. The first uses the symbols ‘greater than’ and ‘less than’ to symbolically represent the unequal association of variables. The latter uses an ‘equal to’ sign to represent the equality of the left and right sides of the equation.
The possible solutions for each are also varied, so that the first can have multiple plausible results while the second has a definite and singular solution. It is necessary to take into account these differences to understand the operation of each of these mathematical forms of representation.