A comparison relationship between two algebraic expressions or quantities is known as an Inequalities.
There are two main types of inequalities:

Greater than or greater than equal to: > or ≥

Less than or less than equal to: < or ≤
Example: 3x + 1 > x − 3 or x^{2} − 3x ≤ 0
As is the case with equations, inequalities are ordered by degree and by the number of unknowns. In the above two examples, the first is a linear inequality with one unknown and the second is a quadratic inequality with one unknown.
Solving Inequations
On the basis of the laws of inequality, there are following working rules.
1. Rule of Addition and Subtraction
Adding or subtracting a fixed number to each side of an inequality produces an equivalent inequality.
Example: Adding 2 to each side of the inequality x – 2 ≤ 1 is equivalent to x ≤ 3.
2. Rule of multiplication or division by a positive number
All terms on both sides of an inequality can be multiplied or divided by a positive number.
3. Rule of multiplication or division by a negative number
If all terms on both sides of an inequality are multiplied or divided by a negative number, the sign of the inequality will be reversed.
Example: If 6x – 4 < – 8x + 6 then dividing by 2, it becomes –3x + 2 > 4x – 3
Solution Sets
The solution of a linear inequation in one variable consists of many real numbers but may not all real numbers. As such the set of solutions is always a subset of real numbers. Solving an inequality means describing a set not just finding a number. This set is the solution set of the problem.
The solution of any inequation is always expressed in a solution set.
1. Ranges where the ends are excluded
If the value of x is denoted as (1, 2) it means 1 < x < 2 i.e. x is greater than 1 but smaller than 2.
2. Ranges where the ends are included
[2, 5] means 2 ≤ x ≤ 5
3. Mixed Ranges
(3, 21] means 3 < x ≤ 21
4. If solution set = {1, 2} means x = 1 and 2 only.
Example 1: Solve for x, –2x > 4
–2x > 4
Divide both sides by –2,
⇒ x < –2