Linear inequalities reasoning – UGC NET Question

Statements A, B and C are correct: the behaviour of inequalities under multiplication by positive and negative numbers is standard, and solving them parallels solving equations with additional attention to sign changes. Statement D is false because solutions of inequalities are often intervals or ranges of values, not single numbers, and E is false because inequality reasoning has many practical applications and is tested in aptitude sections. Therefore the option that includes A, B and C and excludes D and E is correct.

Option A:
Option A is incomplete as it omits C and thus fails to highlight the close procedural connection between solving equations and inequalities, which is a key conceptual insight in aptitude contexts.

Option B:
Option B is also incomplete because it leaves out A, ignoring the important fact that multiplication by a positive number leaves the inequality direction unchanged. Without A, some fundamental transformation rule is missing.

Option C:
Option C is correct because it gathers all three true statements about manipulation and solution processes for inequalities, while rejecting D and E, which misrepresent the nature and usefulness of inequality solutions. It matches the conceptual level expected in UGC NET.

Option D:
Option D is wrong since it includes D, the false claim that solution sets are always single numbers, and thereby contradicts the idea of intervals. Including this misstatement makes the combination logically incorrect.