#### definition

Two real numbers or two algebraic expressions related by the symbol ‘<’, ‘>’, ‘≤’ or ‘≥’ form an inequality.

3 < 5; 7 > 5 are the examples of numerical inequalities while

x < 5; y > 2; x ≥ 3, y ≤ 4 are some examples of literal inequalities.

3 < 5 < 7 (read as 5 is greater than 3 and less than 7), 3 < x < 5 (read as x is greater than or equal to 3 and less than 5) and 2 < y < 4 are the examples of double inequalities.

In this Chapter, we shall confine ourselves to the study of linear inequalities in one and two variables only.