# Mathematical inequality

Mathematical inequality is a proposition of relation of order existing between two algebraic expressions connected through the signs: unequal than ≠, greater than>, less than <, less than or equal to ≤, as well as greater than or equal to ≥, resulting in both expressions of different values.

Therefore, the inequality relationship established in such an expression is used to denote that two mathematical objects express unequal values.

Something to notice in expressions of mathematical inequality is that, those that employ:

• greater than>
• Less than <
• Less than or equal to ≤
• Greater than or equal to ≥

These are inequalities that reveal to us in what sense the inequality is not the same.

Now, the cases of those inequalities formulated as:

• Less than <
• Greater than>

They are inequalities known as “strict” inequalities.

Meanwhile, the cases of inequalities formulated as:

• Less than or equal to ≤
• Greater than or equal to ≥

They are inequalities known as “not strict or rather broad” inequalities.

Mathematical inequality is an expression that is made up of two members. The member on the left, on the left side of the equal sign and the member on the right, on the right side of the equal sign. Let’s look at the following example:

3x + 3 <9

The solution of the previous statement reveals the inequality of expressions.

## Properties of mathematical inequality

• If both members of the expression are multiplied by the same value, the inequality remains.
• If we divide both members of the expression by the same value, the inequality remains.
• If we subtract the same value from both expression members, the inequality remains.
• If we add the same value to both members of the expression, the inequality remains.

Keep in mind that mathematical inequalities also have the following properties:

• If both members of the expression are multiplied by a negative number, the inequality changes direction.
• If both members of the expression are divided by a negative number, the inequality changes direction.

Finally, we must emphasize that mathematical inequality and inequality are different. An inequality is generated by an inequality, but it may have no solution or be inconsistent. However, an inequality may not be an inequality. For example

3 <5

The inequality is met, since 3 is less than 5. Now, it is not an inequality since it has no unknowns.