In mathematics, equations and inequalities are both expressions involving mathematical symbols and relationships, but they serve different purposes and represent different concepts.
1. **Equation:**
- An equation is a mathematical statement asserting that two expressions are equal. It typically contains an equal sign (=).
- The goal when working with equations is to find the values of the variables that satisfy the equality.
- Example: (2x + 3 = 7) is an equation. Solving it means finding the value of (x) that makes both sides equal.
2. **Inequality:**
- An inequality is a mathematical statement that shows the relationship between two expressions, indicating that one is greater than, less than, or equal to the other. It uses inequality symbols such as (<) (less than), (>) (greater than), (leq) (less than or equal to), or (geq) (greater than or equal to).
- The solution to an inequality is often a range of values, not just a single value.
- Example: (3x - 5 < 10) is an inequality. Solving it involves finding the range of values for (x) that make the inequality true.
In summary, equations express equality between two expressions, while inequalities express a relationship of order (greater than, less than, or equal to) between two expressions. Solving an equation finds the specific value(s) that make the equation true, whereas solving an inequality finds a range of values that satisfy the inequality.
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