If and are two quantities such that ; then any of the following conditions could be true:

If and are real numbers, then each of the following is called a linear inequation in one variable:

As you would have noticed already, the signs are called signs of inequality.

Replacement Set and Solution Set in Set Notation

The set from which the value of the variable is chosen is called Replacement Set and its subsets, whose elements satisfy the inequation are called solution sets.

Let’s take the following example:

If the inequation is , if

- The replacement set , then the solution set
- The replacement set , then the solution set

We can also describe the solution set in set builder form i.e or as in the second case

If the inequation is , if

- The replacement set , then the solution set
- The replacement set , then the solution set

We can also describe the solution set in set builder form i.e or as in the second case

You could also represent the above solutions on a number line as well. Please note the following notations:

marks the end of the range with a strict inequality

marks the end of the range with a strict inequality

Therefore, for we can draw as follows….

Therefore for we can represent as follows….

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