An inequality is a mathematical statement that compares the values of two quantities, showing which one is greater than, less than, or equal to the other.
To solve an inequality, you can use algebraic techniques such as adding, subtracting, multiplying, and dividing both sides of the inequality by the same number. You may also need to use the properties of inequalities, such as switching the direction of the inequality when multiplying or dividing by a negative number.
The main difference between solving an equation and solving an inequality is that an equation has an equal sign, while an inequality has an inequality sign (such as <, >, ≤, or ≥). When solving an equation, the goal is to find the value of the variable that makes the equation true, while when solving an inequality, the goal is to find the range of values that make the inequality true.
There are several types of inequalities, including linear inequalities (where the variable has a power of 1), quadratic inequalities (where the variable has a power of 2), and rational inequalities (where the variable appears in the denominator of a fraction). Inequalities can also involve multiple variables and can be solved using graphs or systems of equations.
Inequalities are used in a wide range of real-life situations, such as determining whether a person is eligible for a loan based on their income, comparing prices to find the best deal, and analyzing data in fields such as economics, medicine, and engineering. Inequalities can also be used to model and solve problems in various areas of science, including physics, chemistry, and biology.