INEQUALITIES: AN OVERVIEW OF THE CONCEPT

Inequality in math describes the relation between two numbers to determine the comparable value of the numbers or mathematical expression. Inequality is often used for determining the properties of the two or more numbers by comparing the value of the numbers. An inequality is governed by multiple properties to determine the sharp decrease or increase in the value of numbers. Inequality compares the value to determine the binary relation among the numbers or values in the mathematical equation. If the function of the inequality is strictly monotonic (ab) in the equation, then the relation in the inequality is also strict.

What are inequalities?

Inequalities in math are the process of comparison between two numbers or the variables to identify the strict relationship or monotonic relationship between the variables. There are different notations used to denote the different types of inequalities in math. For example, the notation ab signifies that a is greater than b in the equation. In the equation a is not equal to b means there are strict inequalities in the equation. Strict inequalities mean the value of a is significantly less or greater than the value of b in the equation.

Types of inequalities

In the contract of monotonous inequality, two types of inequality are not strict in the equation. The notation a ≤ b denotes that the value of a is either less or equal to the value of b. Therefore, the value is not strict in this type of inequality in the equation. On the other hand, a ≥ b signifies that the value of a is either greater or equal to b. The relation of a is not greater than bt can also be denoted as the non-strict relationship among the variables in the equation. The notation a<>b denotes that the value of a is much higher than the value of b in the equation. The above relation of inequality signifies that the lower value can be neglected by proper accuracy of approximation in the equation.

The function of inequalities

• Strict inequalities demonstrate the result in the number line where symbols can be easily remembered by comparing the size of the values.

• The transitive property of the inequality signifies that if “ a ≤ b and b ≤ c, then a ≤ c” 

• Although in the case of strict inequality in the equation the result can be signified by “If a ≤ b and b < c, then a < c. If a < b and b ≤ c, then a < c”

•  In the case of determination of the value in the function of inequality, a common factor (C) is added or subtracted from both sides of the equation.

Concept of inequalities in the equation

Determination of the inequality value in the equation helps to identify the relationship between the two variables. The property of the “additive inverse inequality” states that “if a ≤ b, then −a ≥ −b”. Inequality in math helps to determine the result of the algebraic equation where a strict relationship has been described in the equation of two variables. Inequality involves the determination of all possible values in the equation to determine the result of a true statement. In the equation, if inequality is multiplied or divided by factors on both sides then it means it is true in the relation of the equation.

Inequalities questions in math

“The question of inequalities” helps to determine the values of each variable to identify the result of the equation.

For example: If we want to calculate the value of the equation “4(x + 2) – 1 > 5 – 7(4 – x)” then the process can be followed by the below stated equation.

“4x+8-1>5-28+7x

4x+7>-23+7x

-3x>-27

x>9”

Therefore, from the result of the above inequality equation, it is calculated that the value of x is greater than 9.

Inequality identification process

There are different properties of inequality in the equation that determine the reaction of the two values in the equation. “Converse inequality property” in the equation means “a ≤ b and b ≥ a” are equivalent in the equation. Transitive inequality in the equation determines the comparable value based on the nature of the comparable relation of the two variables. The additive inverse property of inequality denotes that the value is either positive or negative to the value of either variable. Sharp inequality describes the sharp reduction or increment in the value in binary relation in the equation.

Conclusion

The above study indicates that the inequality function is quite useful to determine the results of two variables in the given equation of algebra. The strict inequality describes the result of a monotonic relationship among the variables in the equation. Inequality helps to compare values based on the additive inverse rule for determining the exact functional value of the variables.