What are inequalities
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What types of problems can be solved using the greatest common factor?
Inequalities are mathematical expressions that compare two quantities and state that they are not equal. Specifically, an inequality represents a relationship between two values, where one is greater than or less than the other. Inequalities are represented by symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), and "≠" (not equal to).
To understand how inequalities work, let's consider an example. Assume we have two variables, "x" and "y", and we want to compare them using an inequality. For instance, suppose we want to express the idea that "x is greater than y". We would write this inequality as "x > y".
To solve an inequality, we need to find the range of values that make the inequality true. This range is called the solution set. To do this, we often manipulate the inequality using mathematical operations such as addition, subtraction, multiplication, and division, just like solving equations. However, there is one important difference: when we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality symbol.
For instance, consider the inequality "2x < 10". To solve for "x", we divide both sides of the inequality by 2: 2x / 2 < 10 / 2, which simplifies to x < 5. Thus, the solution set for this inequality is all values of "x" that are less than 5.
Inequalities are essential in various fields of study, such as economics, physics, and social science, where comparisons and relationships between quantities play a crucial role. They help us describe relationships such as less than, greater than, or not equal to, providing a powerful tool for analyzing equations and real-life situations that involve comparisons.