A linear inequality equation is a mathematical statement that uses inequality symbols to compare two linear expressions. Here are some examples of linear inequality equations, derived from the provided references:
Examples of Linear Inequality Equations
Linear inequalities, unlike linear equations, use symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to) to indicate a range of possible values rather than a single solution.
| Inequality | Description |
|---|---|
| 3x < 2y + 5 | This inequality shows that the expression 3x is less than the expression 2y + 5. |
| 8y – 9x ≥ 10 | This inequality shows that the expression 8y – 9x is greater than or equal to 10. |
| x + y ≤ 0 | This inequality shows that the sum of x and y is less than or equal to 0. |
Key Characteristics
- Linear Expressions: Each side of the inequality involves linear expressions, meaning variables are raised to the power of 1.
- Inequality Symbols: The use of symbols like <, >, ≤, or ≥ indicates that one side is not equal to the other, but instead is either greater than, less than, or greater/less than or equal to.
- Solutions: Unlike linear equations which often have a single solution, linear inequalities usually have a range of values that satisfy them.
Non-Example from the References
- 9x ≥ 10/y is not a linear inequality, because 'y' is in the denominator, making the expression non-linear.
Practical Insight
- Linear inequalities are used in many real-world applications where a range of values are acceptable or where constraints need to be placed. Examples include budgeting constraints, profit margins, and resource allocation problems.
