NCERT Book Class 11 Maths Linear Inequalities Questions

6.1.1 A statement involving the symbols ‘>’, ‘<’, ‘ ≥’, ‘≤’ is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

(ii) Inequalities which involve variables are called literal inequalities. For example, x > 3, y ≤ 5, x – y ≥ 0.

(iii) An inequality may contain more than one variable and it can be linear, quadratic or cubic etc. For eaxmple, 3x – 2 < 0 is a linear inequality in one variable, 2x + 3y ≥4 is a linear inequality in two variables and x2 + 3x + 2 < 0 is a quadratic inequality in one variable.

(iv) Inequalities involving the symbol ‘>’ or ‘<’ are called strict inequalities. For example, 3x – y > 5, x < 3.

(v) Inequalities involving the symbol ‘≥’ or ‘≤’ are called slack inequalities. For example, 3x – y ≥ 5, x ≤ 5.

6.1.2 Solution of an inequality

(i) The value(s) of the variable(s) which makes the inequality a true statement is called its solutions. The set of all solutions of an inequality is called the solution set of the inequality. For example, x – 1 ≥ 0, has infinite number of solutions as all real values greater than or equal to one make it a true statement. The inequality x2 + 1 < 0 has no solution in R as no real value of x makes it a true statement.

To solve an inequality we can

(i) Add (or subtract) the same quantity to (from) both sides without changing the sign of inequality.

(ii) Multiply (or divide) both sides by the same positive quantity without changing the sign of inequality. However, if both sides of inequality are multiplied (or divided) by the same negative quantity the sign of inequality is reversed, i.e., ‘>’ changes into ‘<’ and vice versa.

Please refer to attached file for NCERT Class 11 Maths Linear Inequalities Questions