Inequalities

An inequalities is a statement, that relates the size or order of two objects or about whether they are the same or not.

Solving linear inequalities is very much similar to solving linear equations, except for one small but important change: you flip the inequality sign whenever you multiply or divide the inequality by a negative number. In linear equation we don’t do that.

Procedure for solving inequalities:

As in the case of solving inequalities equations, there are certain rules for the inequality problems which do not change the solutions. Here is a list of "permissible'' manipulations:

Step1: Adding/subtracting the same number on both sides.

Step2: Switching sides and changing the orientation of the inequality sign.

Step3: Multiplying/dividing by the same positive number on both sides.

Step4: Multiplying/dividing by the same negative number on both sides and changing the orientation of the inequality sign.

• The notation a < b means a is less than b.
• The notation a > b means a is greater than b.
• The notation a ≠ b means a is not equal to b,
• The notation a ≤ b means a is less than or equal to b (or, equivalently, not greater than b)
• The notation a ≥ b means a is greater than or equal to b