Inequality in math
In mathematics, inequality is a relationship between two expressions or numbers that indicates whether one is greater than, less than, or equal to the other. It is represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≠ (not equal to).
Inequalities allow us to compare the values of different mathematical expressions and numbers. They are used to solve mathematical problems, analyze data, and make comparisons in various fields such as economics, physics, and social sciences.
Inequalities can be classified into different types based on the operations involved:
1. Linear Inequalities: These involve linear expressions and variables. For example, 2x + 3 < 8 or 4y - 2 ≥ 10. The solution to a linear inequality is a range of values that satisfies the given conditions.
2. Quadratic Inequalities: These involve quadratic expressions and variables. For example, x^2 - 5x + 6 > 0. The solution to a quadratic inequality is the range of values for which the quadratic expression is greater than or less than zero.
3. Absolute Value Inequalities: These involve absolute value expressions and variables. For example, |x - 3| ≤ 5. The solution to an absolute value inequality is the range of values for which the absolute value expression is less than or equal to a given number.
4. Rational Inequalities: These involve rational expressions and variables. For example, (x + 1)/(x - 3) > 0. The solution to a rational inequality is the range of values for which the rational expression is greater than or less than zero.
Solving inequalities often involves applying algebraic techniques such as combining like terms, factoring, graphing, or using number lines. The solution to an inequality can be a single value, a range of values, or an interval notation, depending on the context of the problem.
Understanding inequalities is important in various mathematical concepts and applications, such as solving systems of linear inequalities, optimizing functions, finding maximum and minimum values, and analyzing mathematical models.