Subtracting a quantity from the quantities on both sides of an inequality is called the subtraction rule of an inequality.
A quantity should have to be subtracted from a quantity on one side of an inequality for either simplifying or solving inequalities. Subtracting a quantity from the quantity on one side of an inequality imbalances the quantity on other side of inequality. So, a special rule is required to subtract a quantity on either side of an inequality and it is called the subtraction rule of inequalities.
The following example helps you to understand the difference rule of inequalities.
$4 < 9$
The number $4$ is less than $9$ and find their difference. $9-4 \,=\, 5$. The difference between them is $5$.
Now, subtract $3$ from the quantity on left-hand side of inequality.
$\implies$ $4-3 \,<\, 9$
$\,\,\,\therefore\,\,\,\,\,\,$ $1 \,<\, 9$
The number $1$ is less than $9$ and their difference is $9-1 \,=\, 8$.
Actually, the difference between the quantities of inequality is $5$ but now, the difference between the quantities of inequality is $8$. It clears that subtracting a quantity from the quantity on one side of inequality imbalanced the other side in inequality.
Now, subtract the number $3$ from the quantity on right hand side of inequality to understand the subtraction rule of inequality.
$\implies$ $1 \,<\, 9-3$
$\,\,\,\therefore\,\,\,\,\,\,$ $1 \,<\, 6$
The number $1$ is less than $6$ and their difference is $6-1 \,=\, 5$.
In fact, the difference between the quantities of inequality is $5$. After subtracting $3$ from both sides of quantities, the difference between quantities of inequality is also $5$. It reveals that subtracting a quantity from both sides of quantities of an inequality is a rule of subtraction.
The following inequalities in algebraic form demonstrates how to subtract a constant $c$ from the expressions in an inequality as per the subtraction rule of inequalities.
A best free mathematics education website for students, teachers and researchers.
Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.
Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.
Copyright © 2012 - 2022 Math Doubts, All Rights Reserved