Compound Inequalities
Compound inequalities are inequalities that have multiple inequalities separated by “and” or “or”. To solve compound inequalities, solve the inequalities separately, and for the final solution perform the intersection of obtained solutions if the inequalities are separated by “and” and perform the union of obtained solutions if the inequalities are separated by “or”.
Example: Solve: 4x + 6 < 10 and 5x + 2 < 12
Solution:
First solve 4x + 6 < 10
⇒ 4x + 6 < 10 [Subtracting 6 from both sides]
⇒ 4x < 4
⇒ x < 1 or (-∞, 1) —–(i)
Second solve 5x + 2 < 12
⇒ 5x + 2 < 12 [Subtracting 2 from both sides]
⇒ 5x < 10
⇒ x < 2 or (-∞, 2) ——-(ii)
From (i) and (ii) we have two solutions x < 1 and x < 2.
We take intersection for the final solution as the inequalities are separated by and.
⇒ (-∞, 1) ∩ (-∞, 2)
⇒ (-∞, 1)
The final solution for given compound inequality is (-∞, 1).
Read More
Inequalities
Inequalities are the expressions which define the relation between two values which are not equal. i.e., one side can be greater or smaller than the other. Inequalities are mathematical expressions in which both sides are not equal. They are used to compare two values or expressions. It is a mathematical expression used to compare the relative size or order of two objects or values.
They are fundamental in solving problems in mathematics, economics, engineering, and various other fields.
In this article, we will learn about Inequalities including their symbols, rules/properties, types, and their graphical representations and others in detail.
Contact Us