## Inequality

### In mathematics, an inequality is a statement that describes a relationship between two quantities, indicating that one quantity is either greater than, less than, or not equal to the other

In mathematics, an inequality is a statement that describes a relationship between two quantities, indicating that one quantity is either greater than, less than, or not equal to the other. It is denoted by specific symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), or ≠ (not equal to).

For example, if we have two numbers, let’s say a and b, the inequality a > b means that a is greater than b. Similarly, a < b means that a is less than b. Inequalities can also involve variables, and we can write equations involving these variables in terms of inequalities. It's important to note that solving an inequality does not give a single value as in equations, but rather a range of values that satisfy the inequality. The solution set can be represented using interval notation or inequality symbols. Inequalities play a significant role in various areas of mathematics, such as algebra, calculus, and optimization problems. They allow us to compare and describe relationships between quantities and analyze situations involving varying conditions or constraints. When solving inequalities, different techniques are employed depending on the type of inequality. These techniques involve manipulating the inequality by adding, subtracting, multiplying, or dividing both sides by the same quantity. However, it's crucial to be cautious about the direction of the inequality when we multiply or divide by a negative number, as it can change the direction of the inequality. Inequalities are widely used in real-life applications as well. They help in interpreting and understanding situations involving measurements, comparisons, and constraints. For example, they can be used to determine the range of possible values for a variable, set limits in optimization problems, or describe conditions for economic or social systems. In summary, an inequality is a mathematical statement that shows a relationship between two quantities, indicating whether one is greater than, less than, or not equal to the other. It is used to compare and describe relationships between quantities, solve problems, and analyze situations with varying conditions or constraints.

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