Class 11 Maths Formula Sheet 2026-27 (Science Stream)

5.2 INEQUALITIES

A statement in which two real numbers, or two algebraic expressions, are connected by one of the signs <, >, ≤ or ≥ is called an inequality. Thus 3 < 5 and 7 > 5 are numerical inequalities, whereas x < 5 and y ≥ 3 are inequalities involving letters. When a quantity is placed between two others, as in 2 < y < 4, we speak of a double inequality.

An inequality in which the variable appears only in the first degree, for instance ax + b > 0, is a linear inequality in one variable; ax + by < c is linear in two variables; and an inequality containing x², such as ax² + bx + c ≤ 0, is quadratic.

Any value of the variable that turns an inequality into a true statement is a solution, and the collection of all such values is the solution set. The procedure for finding it closely resembles the procedure for equations: the same number may be added to or taken away from each side, and each side may be multiplied or divided by the same positive number without changing the inequality. Care is needed with negative numbers, because multiplying or dividing both sides by a negative quantity turns the inequality the other way round.

The solution of a linear inequality in two variables is represented graphically by a half plane.