An inequality is a statement such as "x is less than y" or "x is greater than or equal to y". In addition to the symbols for add, subtract, multiply, and divide, Mathematics also applies standard symbols to show how the two sides of an equation are related.

Mathematical Symbols for Equality and Inequality

An inequality is a statement that uses one of the following symbols:

  1. = : equal to

  2. ≠ : not equal to

  3. ≅ : approximately equal to

  4. > : greater than

  5. ≥ : greater than or equal to

  6. < : less than

  7. ≤ : less than or equal to

Mathematical operations with inequalities

You treat inequalities a lot like equations. Isolate the variable to one side and perform the same operations on both sides of the inequality. The only difference is that if you multiply or divide by a negative number, you need to reverse the direction of the inequality sign. For example,

-2x ≤ 10

x ≥ 5

Working with ranges of numbers

You can also use inequalities to show a range of numbers. For example, the range of numbers between –6 and 12 as an algebraic inequality is like this:

-6 < x < 12

To show the range between –6 and 12 including –6 and 12, you use the sign:

-6 ≤ x ≤ 12

You can add or subtract values within a range. For example, you add 5 to each part like this:

-6+5 < x+5 < 12+5

-1 < x+5 < 17

Transitive Property

If x < y  and y < z, then x < z

Addition of Like Inequalities

If x < y and w < z, then x + w < y + z